It's atypical for a student to go directly from a UC to a CSU or from a CSU to a UC because of the lack of course articulation between them.
Most students at an in-state CA 4-year school will switch to a CCC to be able to take more classes that directly articulate into the program they are trying to transfer to, as well as gain priority admission.
For example, UCSC (the closest UC to SJSU) only has 2 of 13 lower-div classes for the major that articulate to SJSU whereas De Anza College, a California Community College, looks like it has about 13 of 15 lower-div classes for the major that articulate to SJSU.
Source: assist website.
Best, cheapest bet, would be to look into a CCC program and think about a timeline that it will take for you to transfer to SJSU with as many articulated courses as possible.