I would post this question on link below because there are a lot of helpful transfer posters on that transfer thread. You are being smart to ask this question, because USC takes much less AP wise (pretty much just 4 and 5s) than say the UCs (who accept a lot of 3s) and I am not sure if the ones you then take at Palomar will transfer. If they do at all, it may just be elective credit versus applying the credit to a major, and at some point, you just have enough/too much elective credit and you still have to take other courses to meet your grad requirements for your major. Will leave it to the experts here:
http://talk.collegeconfidential.com/transfer-students/1903737-2017-2018-usc-transfer-p1.html
Also, don’t hesitate to call admissions and ask that question (select transfer applicant at the prompt) - not sure how helpful they are on general questions like this and it is a crazy busy time there - but it never hurts to try.