If you stay as an engineer then SJSU is as good as almost anywhere else since the engineering degree is pretty standardized across schools thru ABET. However for Applied Math school name may play a role in who recruits on campus and how a resume is evaluated depending on who the employer is.
Transferring in the end is a personal call but if you want to do it then why not go all in and transfer from a CCC? Instead of returning to SJSU, attend a CCC for a year starting this September. Applied Math is a major at Berkeley, Santa Cruz, Merced, Davis, and UCLA so you could use TAG for guaranteed admission at one school from Santa Cruz, Merced, or Davis and you’d have the CCC boost in chances for Berkeley and UCLA.
Of course you’d want to check the TAG rules carefully to make sure you qualify. And Davis used to require you to have been enrolled at a CCC the spring prior to submitting the TAG application which would make you ineligible. I don’t see that on their website anymore but you should check with them.
Additionally UCLA has the Transfer Alliance Program (TAP) which gives priority consideration for admission to majors in L&S (these days called the “College”) and Applied Math is one of them. Anecdotally online it is said that the admission rate for those completing TAP is 75% or better. More info about the program at UCLA Transfer Alliance Program | UCLA Undergraduate Admission
Berkeley has a separate TAP program TAP | Center for Educational Partnerships which says “the Transfer Alliance Project prioritizes serving community colleges from geographically underserved areas that have been designated as having low transfer rates to the University of California system.” It’s not clear if it will be a boost to you although can’t hurt to look into it.
Lastly it may be worth doing a 5-Year Bachelor’s/Master’s Program in Applied Math which some schools like UCLA have. Typically you don’t apply until you’ve already transferred, I just want you to know it’s out there.