getting SSN is straight forward. You just need to fill the application form and submit it. Since you may get paid for PhD (stipend), you will need SSN. once you join the program, you can apply immediately. It takes 2 weeks to get the SSN. for phone connection, they use the last 4 digits of passport instead of SSN if the international students don't have SSN card. You can do the same or wait till you get the SSN. Banks don't necessarily need a SSN, passport and visa is sufficient. If some banks ask for it, you can wait till you get the card.