Ah, the fun of trying to navigate DMV websites. I see the 60 days you are referring to on the MN DMV website, but the DL for All fact sheet also contains the attached wording (30 days). So I guess my advice would be to go as soon as you have to documentation required to satisfy conditions.
I didn’t see anything specific about SSN (definitely possible I missed it) in the DL for All wording, rather it all seems to be about legal presence. A warning: my experience in WI (admittedly not as liberal as MN) is that if you are eligible for an SSN (eg K1,CR1) you cannot get a DL without one, whereas others who are also here legally but aren’t eligible for SSN can just certify that fact and get the DL. Seems needlessly burdensome on those who are eligible, but those are the rules. Obviously a different state and all, but just trying to illustrate that sometimes the rules aren’t necessarily that intuitive.