I just returned to Germany after J1. Is it too soon to apply for B1 in March to attend a conference?

If you don't have a return requirement based on your J-1 status, then you can certainly apply for a B1-B2 visa. Being approved US consular officials in your home country immediately after finishing the J-1 program has some risk, so you would want to include strong reasons for spending more time in the US, evidence of ties to your home country, how you intend to support yourself in the U.S. without working, and a return flight ticket (although that is not usually a requirement) to show that you are a legitimate visitor. Having a Social Security Number is not a factor (although Social Security Administration records of income while on a B1/B2 visa certainly would be).