I have a mild amount of insight into getting algo trading software engineering jobs: I had an internship at one of these companies this last summer and got a full time offer from from several. (However, I'm planning on working on alignment).
Maybe this is all totally obvious, but regardless, my short summary for one path into this industry is something like:
This means that internships after freshman/sophomore year can be really important.
Of course, ideally, you would just intern at an algo trading place from the start, but these internships can be hard to get without the right prior internships.