Do you believe that Adam and Eve evolved from ape like creatures that preceded them or do you believe they were a special creation?
I believe all attempts to try to harmonize modern science and Scripture commit the error of anachronism by reading back a foreign understanding into the Bible. I believe we must always try to follow standard principles of biblical hermeneutics, meaning interpreting in the proper historical context (which for Genesis 1 is the Ancient Near East).
In short, "what would this verse/passage have meant to them at the time?" If it is an interpretation that the original intended audience would not have come up with, then that can't be the correct interpretation. For example, Jeremiah 10 can't be referring to Christmas trees before there was such a thing as Christmas (that's anachronistic), nor would the intended audience have understood it that way. "Let there be light" can't be a reference to modern cosmology's 'Big Bang Theory." The original intended audience would never think that's what Gen 1.3 is trying to communicate, so that can't be the correct interpretation.
Modern science is a relatively recent development, and our society puts great value in science, so naturally we would like Genesis to answer and accord with modern science, but we can't read Genesis 1 through that lens (that's anachronistic). We must first seek to understand what it would have meant back then, and then we can see how it applies to today.
When we do this we find Genesis 1-3 has little to none to do with modern science. Genesis 1 has more in common with Egyptian pagan creation myths, and indeed reads like a point-to-point refutation of Egyptian pagan beliefs (See, "
Scientific Concordism vs Divine Accommodation").
We also see that Genesis presents a prescientific view of the cosmos. The 'sky' is a solid structure that the sun, moon, and stars are afixed to/embedded "in" below the "waters above" that were the source of rain for Noah's Flood (Genesis 1 effectively locates the sun, moon, and stars in Earth's 'atmosphere'.). The only way I see to maintain the doctrine of inspiration (which I certainly do believe) is some form of Divine Accommodation (since Scientific Concordism doesn't work) (Again, see, "
Scientific Concordism vs Divine Accommodation").
So as a scientist, I actually have a strict keep-science-out-of-Scripture policy, because that is anachronistic and results in interpretive errors. We have to interpret Scripture on Scripture's terms. So, I always compartmentalize and separate the two: what does science say, what does Scripture say, independent of one another? I try to be as fair and honest as I can when answering that question.
Having said that I can now answer your question as follows:
(1)
Scientific evidence indicates beyond a reasonable doubt that humans-primates share a common ancestor.
(2) Scripture does not teach that Adam & Eve evolved from primate ancestors.
(3) I don't know how to harmonize science and Scripture, but if Genesis never intended to give us a modern scientific account (which seems it doesn't, because a prescientific view is presented), then any apparent 'conflict' should not concern us. Importantly, it doesn't change the theological truth (and reality of fact) of the Fall one way or the other. It is also worth noting that Genesis 2-3 combines elements of *both* poetry and prose, and both 'historical' and symbolic elements (it is not either or, but both that we see).
That doesn't mean it's not true. It simply means that common Ancient Near East symbols and motifs and even priestly language are used to represent and communicate a real, historical Fall of humanity. There is much symbolism related to the Tabernacle/Temple. The Hebrew words used to describe Adam's garden tending function are the same used of the Levitical priests, and the gemstones include those on the priest's breastplate. The genealogy in Genesis 5 tells us that Adam and Eve are meant to be seen as real, historical people. But Adam and Eve are also uniquely Hebrew names and so that can't be their actual names (Hebrew didn't exist until after the flood), and their names are symbolic, representative of all humanity. It's like if we were talking about two literal, real, historical people and said "His name is Man, and her name is Woman." That is what we see with the names Adam and Eve. So Genesis is clearly talking about real people, but at the same time also presenting Adam and Eve as representative of all humanity.
I think where we err (today) is in our rigid modern age literal fact OR nonliteral fiction conditioning of the modern age. That false dichotomy overlooks the fact that 'historical narrative' can include exaggerated figures of speech (like we see in Joshua's Conquests), or how poetry can be about literal history (like we see with the biblical songs about the Exodus). Genesis 1 has elements of both poetry and prose, too.
I wish I could articulate it better (and feel like I'm starting to ramble and go far afield of your question), but for what it's worth, all the science vs Scripture talk seems to "miss the point" of what Scripture is really trying to say. We could harmonize science and Scripture and still miss the point of Genesis 1-3 entirely. God just doesn't seem to share our modern concerns (about having factual knowledge), but seems more concerned about communicating who He is and where we stand in relation to Him personally. Whether you agree or disagree, hopefully I still at least made sense with what I'm trying to convey. If not I will attempt to clarify.