Few days to two and a half months. My advice would be to apply for SSN in the SSA office as soon as you arrive in the US. It doesn't matter what option you choose in DS-260, the border control officer advised me to do it in person. I've got my SSN in a week.
When you apply for SSN in person, you will get a document that some employers consider as proof that you have an SSN, or use it as a proof of residence, as it shows the address where the SSN will be sent.
As already mentioned, the employment process, renting, leasing, driver's license, and all of those things take time, so it's better to start those processes in parallel, and this SSN application confirmation helps. Later as you get your SSN you will update all parties waiting for it.