Or I guess it might be more helpful to explain my own views and have someone tell me whether I am an old earth creationist or a theistic evolutionist.
I believe that the earth is around 4.5 billion years old
That evolution and natural selection (guided/ordained by God) is responsible for the variation of species
That Adam was an historical figure and the garden account is historical
That Adam and Eve were the first human man and woman and that Adam is the ancestor of all mankind
This far is theistic evolution.
That the flood was a literal world-wide flood
That the first humans were around 6-20ish thousand years ago (I'm okay with gaps in genealogies)
Neither of these has much to do with evolution.
A literal world-wide flood is contradicted by the same geology that affirms a 4.5 billion-year old earth. If you accept the geology for the age of the earth, why reject it in regard to the extent of the flood?
The text of scripture is consistent with a major regional flood.
As for when the first humans were around, it depends on what criteria you use for "human". The oldest discovered fossil skeletons of H. sapiens are reliably dated to nearly 200,000 years old. OTOH, there is little evidence of human CULTURE until around 35-40,000 years ago--when we begin to see cave paintings and decorative art on tools. Is this an indication of some change in H. sapiens that cannot be preserved in bones? One that would make a difference between H. sapiens who are "human" and earlier H. sapiens who were not?
Normally, biologically, we would treat all members of a species the same, but if being "human" implies something over and above a biological definition, maybe we need to consider that something occurred in the H. sapiens lineage after the physical characters of humanity were established through biological evolution.
Still that is much earlier than 6,000 years and I don't see enough archeological difference to justify separating the cave painters from the first city-builders and writers. Once you have art, you soon have the use of pictures to communicate, then pictographs and writing. So I would definitely lean to 20-40,000 years at a minimum for the first "humans" and then only if one makes a distinction between those who were fully human culturally and those who were fully human physically. And since these were the same species, I am extremely dubious about making any such distinction.
Without that distinction, humanity goes back to at least 200,000 years if "human" is identified with "H. sapiens". And if, like some people, one includes other species of Homo (e.g. neanderthalensis, heidelburgensis, erectus, ergaster) within the realm of the human, then we have a fossil record of humanity of about two million years or more.
So, basically, you need to clarify what you mean by "human" and what, if anything, distinguishes a "human" from a creature that is very similar, even identical, physically but not "human".
It's a bit like trying to decide if Data is a person or a machine.