That's their interpretation of it. It is a belief.
No. It is an interpretation (as everything in science), it is not a belief.
Science is based on observable evidence that does not require faith.
correct.
I can't test millions of years ago because I can't observe it.
Maybe you can't. But scientists can. And yes, they can do this via observation, repeatablly and in the present.
So your conditions as stated in the OP
pro memory
It's got to be testable, repeatable HERE and NOW.
At least that's how I understands it.
But, I'm afraid, you understanding is rather limited. on the plus side, this means you can still improve a lot.
So I don't know why they called it science.
This "not knowing" says more about you than about science.
They can have these theories about it but in the end it's just theories.
Ahhhh, just theories...
I think some other people have answered this better than I can ever do, and let them speak:
(just adding some emphasis)
Scientific American said:
Part of the problem is that the word "theory" means something very different in lay language than it does in science: A scientific theory is an explanation of some aspect of the natural world that has been substantiated through repeated experiments or testing. But to the average Jane or Joe, a theory is just an idea that lives in someone's head, rather than an explanation rooted in experiment and testing.
"Just a Theory": 7 Misused Science Words: Scientific American
Correct.

They are tested. perpetually tested.
What I'd like is for scientists to show me here and now in front of my own eyes, that these things actually happen.
What exactly do you want to see? DNA replicating? A volcano erruption? The spin change in electron rotation? The Zeeman effect? There is quite a lot of "science", you know.
And thinking of it, how do you want to see radio active decay? Or the continental drift, or a Higgs particle, or magnetic fields? Just asking.
And when you have specified what you want, how can we show you that on an internet forum? I think, ypu will have to either satisfy yourselve with a movie on youtube or go to a local science museum.