I'm sorry you got rejected. Life isn't over. Let's take your parents out of this for a minute and look at why you want SJSU so much. For example, if you are from the area and want to stay near home, you've struggled academically, or you've visited SF State and know it isn't the right campus culture for you, then attending a CC in the San Jose area isn't a bad idea. If you don't have a good reason for going to a CC, you may find that you'll grow more if you attend a university, live in a dorm, etc.
There are transfer paths from both other CSU campuses and community colleges. Of course, both require that you meet or exceed the academic standards for transferring. You may be able to transfer after one year, so that is something to look into.
The key to talking with and convincing your parents is to have a well detailed and rational plan.