The problem here is that your two rationales for SJSU don’t really dovetail.
On the one hand, you want to try out the school and maybe switch to CC-to-UC if you don’t fall in love with it.
On the other hand, you want to explore your intended major and figure out whether you really want BME or if you would rather be a CS major (which may not be super easy to switch to.) Looking at the curriculum plan https://www.sjsu.edu/bme/docs/Degree%20Roadmap%20BME%204%20Year%20Plan%20Fall%202020%206.5.20.pdf , you won’t take an actual BME class until sophomore fall, and you won’t take a CS-adjacent class (Programming Applications in BME) until sophomore spring. Meanwhile, CS and Software Engineering students will have started the Intro to Programming sequence immediately in the fall of freshman year.
If you really want to keep both paths open, you may be better off going the CC route, where you can cover the bases for both, in terms of lower-division coursework, until you figure out what you want to do. The downside is that you won’t experience any actual BME classes there.
First of all, find out whether your admission index (however they computed that this year, without test scores…?) would have qualified you for admission to CS (or Software Engineering) at SJSU. Often, switching into a major is only an option for students who would have qualified for it when they applied.
Have you looked at the Biomolecular Engineering and Bioinformatics program at UC Santa Cruz? The BS has two tracks - one is similar to the major you are in at SJSU, and the other is a computation-focused track that includes a CS foundation. https://undergrad.soe.ucsc.edu/sites/default/files/curriculum-charts/2020-10/BMEB-BINF%2020-21_0.pdf If your interests lean more in that direction, this might be a better fit for you. And UCSC is extremely transfer-friendly; you might even be able to pull off an early transfer after one year at CC rather than two.
SJSU is an excellent school, and if you were fully invested in the major you’re actually admitted to, I would urge you to go for it. But the fact that you want to hedge your bets on a CS major makes it a less-good fit. If you think you want the SJSU CS major, attending a CC that offers the ADT in CS could well be a smoother path than starting at SJSU and trying to change majors. But don’t take my word for it; speak to an advisor in the CS department and see what they advise.