I know this is only anecdata, but I graduated from a state school (absolutely nothing fancy) with a biochemistry degree and switched to a programming job a couple of years later. I worked in Perl, Python, and JavaScript mostly for years, while picking up whatever interested me on the side, which included Rust.

The company I joined didn’t expect people to already be rust programmers, and I think about half of our engineers are from non-CS backgrounds. Experience counts for way way more than your degree once you’re a few years into the field.

So, keep an eye out! There’s plenty of stuff out there for whatever interests you, and most programming (even in a language like rust) is not super heavy on meatier CS concepts most of the time.