There's no way someone else can sponsor your visa if you are going to use it to do an internship at UCSF (since that would be illegal) 🙁. I don't understand why they accept you if they do not sponsor visas.
Maybe another option is:
- If you have a tourist visa, you can volunteer.
- UCSF would have to pay immigrations fee for your visa, probably that's the reason why they don't want to do it. Ask if you can do a "donation" for that amount of money and they can sponsor your visa that way. I don't know if this is possible but just ask. You would have to prove to immigration you have enough money to stay and cover all your expenses during the internship time.
I have J1 visa, let me know if you have any other question 🙂