First, let's understand something. The Bible was never intended to provide a scientifically accurate explanation of anything. God gave us the Bible to reveal Himself to us and to provide instructions for life and to show us the way to everlasting life. When God revealed the origins of the universe to Moshe (Moses), He did so in the language understood by Moshe, and provided descriptions of events in terms Moshe - and people in general - could comprehend.
When God told Moshe that He created light, He did not say "...And light consists of photons of energy that will confound scientists for Millennia while they attempt to determine whether light is a particle or a wave." God simply told Moshe He created light and that it was to separate the darkness from the light. That was good enough.
When God told Moshe that on the second "day" He created the dome and called it "sky", He offered no other scientific explanation of how or why he separated the waters or that the sky would consist of multiple molecules of a variety of gases which would be beneficial to man and beast, nor how the atmosphere would carry storms which would aid in the distribution of seeds and create an "ecosystem". None of the details would have been important to Moshe.
You see, God only revealed what He needed to reveal so Moshe could teach his people and that they would begin to understand God. Moshe did not have the necessary working knowledge at the time to handle any more details, and neither did anyone alive at the time. But, as you can see, the level of knowledge was not important since the purpose of the revelation was for the understanding of God, not for scientific details.
What is science good for?
Now, let us come to some understanding of what science is good for. Science describes. That's all. Science does not "prove". Science, in fact, does not "explain". Example: Science has described the constituents of an atom. Science has found that an atom consists of protons, neutrons, and electrons, and indeed, more particles which science has called "fundamental particles" carrying names such as "quarks", "bosons", "leptons", "strange", etc. These are nothing but "descriptions" of characteristics observed, and serve to allow science to describe how these "particles" interact. With these "descriptions", science can combine certain "predictable features" (that is, behaviors we have observed and can make the behavior happen again) and provide humanity with something useful such as an "automobile" or a "penicillin", or something destructive like "dynamite".
But above, I said science does not "prove". What did I mean by that? Let's take the "quark". The quark is one of the "fundamental particles" found by science. An actual, physical particle may or may not exist. We don't know. All science really knows is that experiments conducted on atoms provide observations of behavior that seem best explained if a particle exists which would cause that behavior. Then, giving the "particle" characteristics explaining the observed behaviors, the "particle" described begins to look like it is "the answer" and that such a particle must, therefore, exist. We have not proved the particle exists; only that we have observed repeatable behavior that is explained if such a particle were to truly exist.
This is all well and good, because it allows science to "predict" behavior of things that rely on our observations of the "fundamental particles", and thus turn the observations into something useful. "Quantum computers" are a possibility in the future because of predictable, but unproven behaviors. This is nothing greater than what Ben Franklin did centuries ago when he experimented with lighting to determine that it was "electrical", and what Thomas Edison did when he applied his observations on how electricity behaves to make practical products that use the electricity to operate. But realize that, just because science says that a "fundamental particle" exists, and that we can call it a "quark", and that it can explain observed behaviors in the atom, does not explain where the "quark" came from in the first place! Science does not explain. Science only describes.
Science is good for describing how things interact, how molecules behave, how metals can be blended, how water is carried in roots, how medicines work, etc. Since science relies on observation, certain observed variables must be considered as a "benchmark". By "benchmark" I mean a "scale" chosen because it applies to all the things you are measuring. One can use a ruler to measure the length of all objects, thus allowing you to compare the sizes of objects to each other, say the diameter of a quarter (coin) as compared to that of a dime. But one cannot, at least conventionally, use a ruler to measure water. Dipping a ruler in a glass of water cannot tell you how much water is in the glass. To do that we must properly use the ruler and measure instead the dimensions of the container in which the water is held. A ruler therefore is a "benchmark", but only if applied in cases where the scale used is actually applicable.
Take for example, the "light-year". The light-year is a "ruler" and is the "standard" by which science measures distance in the universe. It is the "benchmark" of length for astronomical distances. The light-year, for those who have never heard of it, is the physical distance traveled by a beam of light in one year. For those mathematically minded of you, that is 5,865,696,000,000 miles, or 9,460,800,000,000 kilometers long. So if the nearest star besides the Sun is "4.2 light-years" away (Proxima Centauri), then one has a way to compare the distance to the another star which is 6.0 light years away (Barnard's Star).
Using the "light-year" as a cosmic yard stick is perfectly acceptable for comparing celestial distances. But, a huge mistake is made when one takes the estimated distance to a celestial object (using light-years or any other measurement scale) and concludes that because distant objects are so far away, that the universe itself must be old enough for light from that object to have reached us. This is a conclusion one cannot really make, because it is an extension of the "measure" where the measure cannot be applied! Because the distance to the farthest objects in the universe have been "observed" to be "billions of light-years" away does not lend itself to the conclusion that "therefore the universe is billons of years old".
Let's do a "Gedanken Experiment"
Let's try to demonstrate why this is so. We will do a "Gedanken experiment". "Gedanken" is German for "thought" so a Gedanken experiment is a "thought" experiment. Such experiments are common in the physics community, to help explain some observed characteristics and to defend a theory. A Gedanken experiment allows one to apply known physics to a case and ask a question about the expected outcome. A Gedanken experiment is useful to question a physical observation in a case where one might not be able to make a physical observation or measurement, and yet, draw a valid conclusion.
Here is our Gedanken experiment: I blindfold you and take you into a room where you have never been before. Your instruction, once the blindfold is removed, is to bring back a complete physical description of what you observed in the room. So, into the room you go. The blindfold comes off and you start your observations. You are a very capable scientist, and you set out making measurements. You find that there are a number of objects suspended, magically, in the room and that they are all moving. (Never mind how these objects are suspended in the room without strings - it does not matter, this is a Gedanken experiment!)
As you measure the speed and direction of each object, you tabulate the results. In the end, you realize that all the objects are moving away from the same corner. In fact, you observe that the objects farthest from the corner, based on their speed, tells you that they left the corner about 180 days ago. Further, the objects in the middle of the room, based on their speed, indicates they also left the corner 180 days ago. Further measures on all the objects provides more evidence that all objects left the corner 180 days ago. When you are finished, you exit the room, and being the dutiful and astute scientist you are, you report the details of your findings. You report that there was some sort of event that took place in the corner of the room, and that that event took place 180 days ago, plus or minus 4 days, based on the standard deviation of your measurements. Of this you are quite certain. You are very proud of yourself and you write scientific papers for other scientists to see so you can further your cause to find out the "origins" of the contents of this room.
The only problem is you are wrong. How can that be? The actual "age" of the contents of the room was 2 hours. Two hours earlier the room was empty. But you measured the properties of all the objects in the room! You could not be wrong! Everything in the room left the corner 180 days ago! All your measurements prove this! Wrong! Your measurements only serve to compare the observed behavior in the room. You made a false conclusion when you used your chosen scale (the speed of the objects) to determine the age of some event which you assumed took place in the room. You used your scale in an application beyond where it was valid.
You see, what you did not know is that only two hours before you entered the room, the room was empty, and that I entered the room and placed all the objects in the room and gave each one of the objects the speed and direction of motion such that all objects would appear to have come from the corner. Your measurements were not valid for determining age. Your measurements were only valid for determining the speeds of the objects in the room compared to each other.
Your extrapolation of the speeds back to where the origin appeared to be was false! You were missing the key. The key was the absolute scale. You were not given the absolute scale, so you chose what you thought was the absolute scale. In this case, given the absolute scale, you would have only been able to conclude where the objects were two hours earlier. You would have known that you could not extrapolate your measurements further back in time.
This is the dilemma in reality. When science measures the distances and consequently the age of the universe, they are missing the key. That key is the absolute scale. We don't know the absolute scale. The above Gedanken experiment was constructed to show that the age of the universe is not derivable from the observations. Thus, when science says "the solar system is 4.5 billion years old" science is misapplying the observations. They have extrapolated using a scale which provides invalid results because it has been used outside its region of applicability.
All science can really say is that based on the observed behaviors of celestial objects, assuming there was not some other event that caused the characteristics we are observing, it appears objects in the universe originated from some point. That point seems to have been many billions of years ago but, we cannot, with certainty, conclude the observations allow us to derive a valid age of the universe because doing so, we have applied a scale which is missing the key, i.e., the true scale of time. The objects we are observing, may, in fact have been brought into existence with these observed characteristics. This last statement is something scientists fail to recognize.
Now, in case you have gotten lost, what I have said, is that the observed characteristics of the objects in the universe can only be used to compare objects with each other. To take observations and conclude an age of the universe is a misapplication of the scale you chose. You don't know the absolute scale with which age can be measured!
Thus, there is no problem of inconsistency between the Bible and science. Science has only identified that observations seem to make it appear that objects are millions of light-years apart and that this information is useful to us in terms of future space travel. Fact is, the universe very well might have been created 6000 years ago, just as the Bible seems to indicate, but was created such that the observed characteristics of celestial objects make it appear the universe is many billions of years old when we compare physical things against physical things.