The fact is that evolution defends and insists that the age of the earth is 4.5 BILLION years old,
On one point I agree with you, if the age of the earth is wrong by a factor of 1,000,000 then evolutionary theory has a problem explaining what we see.
One way to handle this "compartmentalization" would be for you to tackle the age of the earth issue first.
A place to explore this might be:
Message 1It is a bit over the usual 300 post limit but it's still open.
The correlations there have never, ever, anywhere been answered. You can be the first.
and it accepts that life spontaneously appeared from the primordial ooze,
This part is irrelevant. If life didn't arise spontaneously but was magicked up by a god, delivered by aliens or whatever evolution is exactly the same. Evolution talks about change in biological populations -- the theory doesn't give a rats ass where the populations came from.
As has been pointed out to you, geology works just fine without evolution. (it uses index fossils but those are independently confirmed first and they are used just because they are convenient not because they are fundamental to geology). Cosmology works happily too.
Nothing rests on an assumption about the way life arose other than that part of chemistry concerned with origins of life.