I think I can use deductive reasoning based on premises which are assumptions of science.
So I think an assumption of science is there are infinite possible ways the world could be.
This sounds more like metaphysical wibble and not at all like a requirement for doing science. How would doing science be different if your assumption was not the case?
There would be no variables, hard to imagine science without variables.
I think we are mixing two concepts here. I’ll call them ontological possibilities and epistemological possibilities. Since we do not have complete knowledge (hence the drive behind doing science) we have unknowns, we have variables. These are epistemological possibilities. I’d call this a motivation for doing science, not a premise.
I took your proposed premise for science to be about ontological possibilities - an assumption that the world could have been other than it is (regardless of our knowledge of it). I do not see how this is, or needs to be, assumed for doing science. It seems to me the world would look the same to us in all respects (ie. as it is) regardless of whether it could have been otherwise or not.
How do we decide whether or not to accept a premise? I’d say it’s based on coherence with observation - which is what science is about. So I’m a bit confused about the notion of a premises for science.