You will go online to ssa.gov and create an account a few days after you arrive and then apply for your SSN online via the SS-5 form. Once you submit this, it will tell you that you have to complete the application in person at an office and should provide you a link to schedule an appointment at your nearest office. Do that and by the time you go to the appointment, you should be all set in regards to the DHS & SSA databases being in sync. Bring a copy of your I-94, your passport with K-1 visa in it and your birth certificate.