I'm going to try to take another approach to answering this question:
Scientific progress is apparently about two (closely related) things: poking and prodding in order to figure things out, and making useful models.
Whether you're a materialist or not, you must notice that it's much easier to poke and prod matter than it is to poke and prod whatever nonmaterial thing you might propose, like souls or ghosts or whatever. So to the extent that science is about poking and prodding, of course it's about matter. That doesn't mean matter is necessarily the only thing that exists, but it means there isn't a whole lot of science we have so far been able to do on things that aren't composed of matter.
The second is, when it comes to models, our history is FILLED with detailed models of physical things, many of these models detailed so well that we can produce compelling computer simulations of those things - small scale quantum events, atoms and molecules and chemistry, planetary physics. We can make computer simulations of these things, and those simulations work because our models are detailed enough to make algorithms to compute them.
Meanwhile, what models are there for the non-physical explanations of things? What model is there of the "substance" souls might be made of, for example?
So it's not so much that materialism itself - the belief that only material things exist - is essential to scientific progress. It's more that the operative ways science functions - via poking, prodding, and models - have so far really only worked for matter, because non-materialists have not developed ways of poking, prodding, or making models of non-material explanations.