Genesis and the big bang theory go hand in hand.
B'reshit bara Elohim et haShamaim v'et haAretz.
So far this is true. (In the beginning G-d created the heavens and the earth.)
Genesis and the theory of how the solar system [works] also go hand in hand.
That is true. Genesis is a bit earth-focused, but why wouldn't it be.
Noah could not have taken 2 of every land animal on the ark.
True. Noah didn't bring cangaroos, for example.
he could however take two of every type of animal ie two elephants not two Asian and two African. two deer not two caribou and two moose.
The text is a bit unclear. Noah was commanded to bring two or seven animals of each type. I assume they were his farm animals. He might have owned elephants. But he probably didn't keep them on a boat. He and his family probably survived the flood on a mountain top or other high-lying region. He probably used a boat to find out who else escaped the flood.
I don't think he had deer.
The flood was highly local, affecting, depending on what flood it was, today's black sea region (which was a fertile valley containing lakes 6000 years ago) or Mesopotamia (today's Iraq).
meaning after the flood there was a whole lot of evolving going on.
Not a whole lot, since the flood was only a few thousand years ago.
But I can see the argument, which is well-made. If Noah brought two of each animal and we have so many species now that two of each would be too many for any boat, there must have been creation of new species after the flood.
Since the Bible doesn't mention creation of new animals after the flood, those must have evolved from existing, already created, animals.