I have no specific experience in regards to UCSD but some experience with other UC’s instead. In general, any student needs to advocate for themselves and will not be handed a job or internship. It is up to the student to seek out their academic advisor and make the academic connections such as taking advantage of Professor office hours. Large class sizes are seen mainly with the GE type courses. Once the students get into their upper division major classes, the class sizes are much smaller.
All schools have career centers that will help with resume writing and interview skills along with job fairs and job postings. However, it is really up to the student to do their own research and find internships and jobs on their own.