How does science work in a random chance world?
It wouldn't. Nor would it work in a universe where a supernatural entity could come in and change things around by fiat, or make things appear counter to how they actually happened.
There is no reason to posit a "random chance world" when we have physical laws that constrain the possibilities.
What we have studied for hundreds of years could change tomorrow in an evolutionary worldview.
Tentativity is the hallmark of science. If something we have been studying for 100s of years has been shown to be wrong, then doesn't it make sense for us to change our mind?
If you mean, gravity could stop working or something preposterous like that, then you're wrong. For one thing, evolution has nothing to say about any of that. For another, if things could turn on and off like that, then our science would be completely wrong, far from being a necessary outcome. You seem to have little to no idea what science is and how methodical naturalism works.