SSA will not issue a number before your work authorization exists verified
The Social Security Administration requires evidence of current, valid work authorization before it will assign a number for work purposes — a job offer letter is not enough. For an H-1B, L-1 or O-1 worker this means the petition must actually be approved and your status must have started; for an F-1 student on OPT it means your Employment Authorization Document must already be in hand. Applying earlier does not speed anything up — it produces a rejection and a second trip to the office.