1 - There was a beginning from "nothing"
Irrelevant; possible with or without the gods
2- The Universe is indeed finely tuned
Irrelevant; possible with or without the gods... even most mythologies with creator-gods, including the Judeo-Christo-Islamic one, don't imagine a finely tuned universe.
The Bible clearly says the Earth's surface is the bottom of the inside of a bubble at the bottom of a great abyss full of water which would collapse on us if not held up/back by the solid dome we call the sky. Others include other ways the world is waiting to be destroyed at any moment, like the one about the world as a carpet held down by giant animals around the edges who cause earthquakes with even small movements and would let the whole thing completely fly loose if they just got up... or the one about how the sun must be driven along its path each day lest it stray too close or stay too high too long and burn everything away... or the one about how the world is in the middle of a constant struggle between the forces of hot and cold, either of which would kill/destroy it all if it dominated over the other even slightly for too long. I don't know of any culture anywhere whose mythology has ever associated gods with a finely-tuned universe; it's more typical to describe and define gods in terms of their relationship to how it's always on the brink of destruction.
A finely tuned universe would consist
entirely of a vast mostly-flat surface extending for any arbitrary distance horizontally, plus or minus a few thousand feet vertically for hills & valleys, with any number of small suns cruising around not very far above, like 20000 feet up and 100 feet wide. In other words, no great forces of opposite kinds of destruction constantly balanced in the struggle over which one gets to destroy us, no demons & monsters prowling prowling for a chance to ruin everything for us, no heavenly booby traps just for gods to conveniently be able to spring on us when they have a temper tantrum, and no space wasted on anything that doesn't contribute in some way to life.
3 - Rather than being "dumb matter" the Universe is predisposed to create Intelligence
Only if by "predisposed" you mean natural selection can have that result but doesn't seem to experience any particular compulsion toward it.
4 - Even if one can see the evolutionary line, the "motor" in the flagellum is remarkable, and the odds are against it
Feelings mean nothing, actual mathematically factual odds mean nothing, and made-up "odds" that aren't really odds at all but just feelings also mean nothing.
5 - The "gears" on a particular insects legs are also remarkable
Feelings mean nothing.
1 - Some people have experiences that science has (very) weak answers for
Irrelevant; even if science had no answers of any kind at all, that would still not be evidence for the gods. It would just be something unknown.
2 - Some people (the prophets) have experiences that change history
In other words, something that consists of nothing but aggregate human behavior can be changed by prominent humans' behavior. How would it even be
possible for this rather obvious fact to have any relevance at all to the existence or non-existence of the gods? This is like trying to prove there's no such thing as bananas because my mother's cat prefers fish over poultry.
Science used to assume that what people saw, heard and touched was hard reality. Science has shown that matter pops in and out of existence, that spooky at a distance can happen, and that the Matrix mind is a logical possibility.
Again, nothing that has anything to do with the gods in any way at all.
They argue that since they have not had "experiences" that are remarkable (despite some stories that I do not accept as remarkable) others do not have such experiences.
Nobody has claimed that. You are lying.
The problem with religious/spiritual experiences is not a matter of whether they happen at all or not but simply the known and well proven fact that such experiences can be misleading and misinterpreted.
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