I don't know what you mean exactly by experiments, but science does not require phenomenon to be directly observed in labs for explainations of that phenomenon to qualify as science.
For example paleontologists study past life by looking at bones - by doing so they are indirectly studying past life. In a way studying bones IS a kind of experiment. It is certainly repeatable - another paleontologist can repeat the study using the same bones. In this way a paleontologist can reach the conclusion that a certain fossil bones belong a reptile for example. Noone reproduced the reptile in the lab, but it's still science.
Seeing as evolution is partly based upon fossil evidence of this kind then it certainly qualifies as a science too.
Long term evolution is not. The further you go back in time, the less direct any repeatable experiment is until you are left simply looking for clues to fit your model, like historians do.
But long term evolution does not have to be directly observed to conclude that it happened, anymore than dinosaurs have to be directly observed to conclude that they happened. Geology, Archeology, Cosmology and Paleontology are all historical sciences which all rely on observing present evidence to test hypothese about the past (effectively therefore performing experiments). That makes them definitely science.
The study of prophecy in scripture seems to qualify under your loose definition. The experiments are trying to date the manuscripts--through language, carbon dating or whatever.
For instance if one accepts that Daniel was written by Daniel, it pretty much proves God. The secular view is that it was a fraud written centuries later...because the prophecies being too specific and accurate to otherwise discard.
But my own internet searching has produced amazing differences of opinion about what qualifies as science. People pretty much contriving that what they prefer qualifies.