Prove what, that they happen or how they happen? Miracles don't require god. You misunderstand the meaning. They just require being unexplainable.
Prove Jesus rose from the grave.
You're right, pretty hard to 'prove' at this point even if it was provable when it occurred. Its roughly the same as 'proving' the big bang happened at this stage. Its pure conjecture based on some evidence. If you think otherwise, how sad you are.
Hell, Prove Jesus ever actually existed.
Lots of evidence that someone like Jesus existed. His feats are another story, but most historians agree that someone like that existed.
Prove that humanity came from a single breeding pair.
Okay, science does that already and doesn't require any religion. When you figure out which came first, the chicken or the egg, then you'll understand why this is true. Eve or no Eve.
Find the genetic bottleneck in our genes from when the world was reduced to Noah and his family.
Thats hard this far after it happened but science is fairly confident the humans on the planet were reduced to at least as low as 10k people at one point. Guessing beyond that is just too much guessing to be called science, but it is possible and it too doesn't require a god.