So what type of proof is being used here huh? Scientific "proof"? Ie "evidence beyond doubt"? In which case evolution common descent is scientifically proved.
Microbial theory, the notion of the existence of microbes
Wrong. The notion of the existance of something is not an explaination, and so cannot be a theory. You probably meant "Microbial theory of disease" aka "Germ theory of disease", which states that disease is caused by microbes. This was clearly not "proven when a microscope powerful enough to see them was developed and used".
Futher the theory that the sun is the center of the universe was easily evidenced when we were able to send a satilite there to send photos.
LOL was that because there is a signpost next to it saying "Center" that required a satellite to read? If you position Earth as the center of the solar system so that the Sun circles the Earth then the path of nearby planets form epicycles. How do you "prove" that is not the case?
frankly there's myriad ways Evolution could be proven if anyone was interested. For isntance a closed environment breeding apes until they all lost the tails, and started talking.
How would that prove evolution? It wouldn't. It would not prove any historical aspect of evolution. It would not prove common descent. All it would prove is that in a closed environment apes can be bred until they lose tails and talk.
Frankly if evolution can do this randomly selective breeding should be able to do it easily and quickly.
The main drawback is that to replicate 1,000 years of evolution you would need 1,000 years of lab time. We might as well sit back and wait 100 years for computer simulations of organisms to be possible and then simulate 100,000 years of evolution in a few minutes.
How is it you would try to use math to support a theory with no mathmatical evidence, or you assuming every science involves math, either way you've clearly been out of college so long, the mold on your brain is replacing your missing hair.
You can quite easily using radio telescopes take photos of the cosmos over time. At which point the relative center should be obvious. Hint it's not you and your little monekies turn into people brain.