You state the problem well. Evolution and our understanding of the bible cannot both be true.
I find that the bible is true when it deals with the most important issues of my life. I find the bible to be true when it can be referenced to witnesses and testimony. I find the bible to speak directly to my heart with a pure sense of truth.
If genesis describes a 6 day 24 hour creation with man being created by God in his full human form and science describes a multiple billion year time frame and man starting from a primeval soup developing randomly rather than purposefully I am confronted with a major dilemma. How do I reconcile all of the truths in the bible that I have tested with the fact that evolution is directly contradicted by the very first chapters of the book of truth?
Do I misread the 6 day creation and do not understand the writing correctly because of preconceptions about the words or do the scientists have incomplete knowledge about the physical world (not a surprising concept based on history and their own statements) ? Or some combination of the two?
Nowhere does the Bible date the age of this earth. Genesis 1:1 declares a statement of fact. Verse 2 continues with 'And' something happened to make this earth become without form void and flooded. Flesh man had not yet been formed.
The earth itself is filled with evidence of it being of OLD time. And Peter that one elected to build the church says there are three different heaven/earth ages. IIPeter 3
Peter also tells us how the Heavenly Father marks His time that a 'day' is as a thousand years. So there is no scripture basis to say the days of creation were 24 hour days as we calculate a day to be today. Man can approximately calculate 6 thousand years since the formation of 'the' Adam into a flesh body through the listing of 'the' Adam's genealogy. Have you noticed anyone missing in 'the' Adam's genealogy in Genesis 5?
I Timothy 6:20
Guard what was committed to your trust, avoiding the profane and idle babblings and contradictions of what is falsely called science