You have to be in the US for 10 (ten) days before you can apply for a Social Security Number.
However, as soon as you can, apply for one as a lot of official forms will need this number. Note though that you will need to give a permanent address in order for the SS office to post your card to you. The State College Social Security Office is at 901 University Drive (see map below), a ∼ 15 − 20 min walk from Davey and is open 9am - 4pm, M-F. Once you have been assigned a SSN (usually a couple of days after you applied) you can get a signed and stamped piece of paper with your new SSN number on it. Having this temporary fix, is generally okay for most forms (*not* for a Driver’s License, see below) but getting the actually SS card is key. In general (and for me) applying for a SSN was relatively painless. Details on:
A spouse / dependent on a J-2 visa will not be able to get a SSN without first obtaining a work permit. They can, however, get a letter saying that they are not eligible for a SSN which can be used to get a driver's license.
