I am just presenting a simple Biblical argument that states the events that occur in Genesis 1 happen before the events of Chapter 2.
Well, one does come before two... but are you saying that there were two creation events, then?
Do you know that according to history Chapter 2 was written before Chapter 1? They're different accounts of the same event that cover different aspects and details of a singular creation. It's not one event happening after the other.
Men and women were created in Chapter 1 and Adam and Eve were created in chapter 2. If you accept this simple biblical logic, this coincides with recent findings that all men alive are genetically descended from a single man, and all women are descended from a single women. Other men and women were existing at the time of this common descendant (Y chrome Adam and Mitochondrial Eve), which is what the Bible says.
Wrong. Y-chromosomal Adam and Mitochondrial Eve were not contemporaries - that is, they lived at very different time periods. They couldn't be the Adam and Eve of the Bible.
Men and women, I believe through natural mens lived prior to Adam and Eve.
Okay, but Adam is literally the "first man".
This eliminate the conflict between evolution and Genesis.
Not really, but there's no need to do that.