There are many who seek to drive a wedge between these two sources of opinion. They are generally scientists who are also militant atheists. Often starting in their reasoning with the arguments between Galileo and the Roman Catholic Church concerning the position of the Earth in the solar system and indeed the cosmos, they see science as the stuff of logic and proof, and religion as the stuff of naive credulity.
This is not reality. In reality, science is a continuum of beliefs about the nature of reality from the readily demonstrable through to the tentatively held hypothesis. In other words, not all science is well agreed upon or widely considered reliable. So there may be realistic 'give' in the scientific outlook, areas where we have to admit that we do not know all the answers.
Scientific or naturalistic reductionism is the discipline which attempts to explain everything merely by logical processes which can be observed, characterized and understood. Such an approach ends up saying that everything is an accident that came from nothing. Our very conscious experience is an illusion.
I am not saying that the scientific method is wrong or bad, I am just saying that it must have limitations somewhere as we attempt to describe the big picture of reality. I have set some of these limitations out in previous posts.
If the Bible is indeed the Word of God, the creator, we need to look at how we might reconcile a Biblical view of origins with a scientific one. Since this is widely seen to have failed, I am looking for legitimate flexibility in both camps in order to reach a harmony.
How much flexibility is there in the scientific opinions about origins? Just how reliable are the theories about origins? Here we are talking about Big Bang Cosmology, by which the heavens and earth, the latter seemingly pretty insignificant, were formed, and the Theory of Evolution by Natural Selection, which seeks to explain the development of sophisticated life on Earth. How well-defined and how reliable are these theories?
On the other hand, what if the Bible is our starting point? (Why do that you ask? Many reasons, two I will give here. Because there is solid logical evidence for the resurrection of Christ, and because the Old Testament lines up well with other disciplines.) How much flexibility might we reasonably allow in our interpretation of Scripture in order to reconcile it with at least some of the conclusions of the scientific communities? For example, can we allow for the possibility that the initial creation account in Genesis Chapter 1 is allegorical and poetic, rather than a literal time line? Can we allow for the possibility that the six days of creation were 'day-ages'? (I use the phrase 'day-age' to mean a period of time described loosely as a day, but actually referring to an epoch. An example would be; 'the day of cheap fossil fuel is over').
Can we allow for the possibility that there were previous tranches of creation on Earth prior to the present one? This is commonly called 'the Gap Theory', because it implies that a great deal happened, in terms of creation and destruction, between Genesis Chapter 1v1 and v2. God created the heavens and the earth. Then a lot happened regarding which Genesis 1 is silent, and then the earth became void and without form.
If we take this 'gap' theory on board, we can interpret the fossil record differently to a young earth creationist who argues for a literal reading of Genesis 1 and therefore an earth which is around 6000 years old. There is more flexibility when it comes to setting the dates of rocks and fossils.
When we read the Genesis account of creation, we are reading an account written in a non-scientific age. We should not be expecting a discourse including for example radiation energy and dark matter. We are looking for a representative description of how things came to be, for a framework from which to proceed. We should not be surprised if the author (ultimately God) uses techniques which simplify things, or even employ cultural assumptions from those times when the story was first told and written. The simplification is for the benefit of the reader, not because the author is ignorant or hiding.