There are basically TWO views on TE:
God directly directs evolution.
God has instilled in living cells/organisms the ability to evolve.
The differences is the view on how random the mutation process is in evolution.
These two are typically, the main views on TE in regards to God involvement in evolution and it must be noted that NO TE view supports the deistic viewpoint.
Those and also the belief that God installed souls into the already resulting and evolved beings, Adam and Eve. Which begs the question, IF true, does humanity have two separate lines - those who sprang from Adam and Eve's linage and those that sprang from their evolutionary ancestors? Or was the other line, those only springing from those on the Ark, the only genetics that survived? And, of course, did the two, pre-flood lines intermix? Of course, as I do not believe man evolved from higher animals, I don't believe this. But IF the differences between Genesis 1 and 2 have to do with a pre-Adam race that was created separately and before Adam and Eve, meaning that the Garden of Eden was part of but separate from the rest of the creation (that also came before it), I am at least open to that possibility. But I still don't believe that means the previous race evolved.
Of course, IF it could be proven that evolution occurred, that this was God's mechanism for creation - and that happend to be true, it really doesn't change anything, in the sense that God still had to begin the universe and install life on earth. But as I always say, if Adam and Eve weren't actual people, then much of Scripture has to be doubted - a very slippery, dangerous and, I think, illogical slope.
The Adam and Eve story, taken as it is written ( if we didn't have Genesis 1 for example), talks to us about two specific people, in a specific place at a unspecific time in history.
One can argue about the geneologies in the rest of Genesis, but that is a different story, why?
Because the Adam and Eve story does NOT give us a time line in regards to WHEN Adam and Eve were created or HOW LONG they were in Eden OR what was happening outside of Eden.
We can postulate/hypothesis something like this: ( and no this specific view has no direct or explicit biblical backing)
God creates the world.
God creates Eden and a garden within it.
God creates Adam and places him in the garden.
Adam goes about his business as per God's plans for him ( naming animals, tending the garden, etc)
God creates Eve from Adam to be his companion.
Time from for all the above? years? centuries? millennium? the bible is not specific so...
In the mean time, other life continues outside the garden and outside Eden, other humans come to be and populate the Earth.
Eventually Adam and Eve screw the pooch and get kicked out of the Garden and Eden and settle elswhere.
Have kids and the geneology of Israel is started...
Cain kills Abel, flees to an existing city and settles down there and gets hitched, has kids, etc, etc..
See, what we do have in the bible is the history of Israel ( comments about other races and civilizations happen only because of interaction with Israel) and that is why the lineage of Adam is crucial because Israel is the race that God started and took under His "wing".
There is a reason that the Bible doesn't speak of the peoples of Russia or China or the Americas or Indonesia, etc, etc.
The bible stories are about Israel and those that came in contact with Israel and, eventually because of Christ, it becomes about US ALL.