jv, I was thinking about your question, and it occurred to me that there were several milestones that happen pretty quickly. I thought I might pass them along so you could be watching for them. For me, I focused on rhythm initially, and not everyone is going to do that. If you do, here's what you might expect.
The first one is that it takes some time to get used to such a tiny instrument... how to hold it (I use a strap, even when seated, even though I do "hold" the instrument more than a guitar), how to pick it and how to navigate such a small fretboard. Ben's introduction to mandolin series is a wonderful resource for that. I refer to it often to help ensure I am not picking up bad habits. I think you will stop thinking about those basics as much within just a few playing sessions.
The next milestone is playing some open chords. It's fun just whanging away on them, and they are easy to pick up. You can hammer-on and embellish them with altered notes and have a great time. To get a few open chords down, my wife did it in minutes and was playing along with me in her first sitting. I think three or so open chords are discussed in Ben's rhythm vid.
At this point, add the knowledge that you can do what verneq called a "no chord chop," and you have enough in your arsenal to make some fun music. So in answer to your original question... If you play regularly (like many do when they get a new instrument) I think you will be ready to play with others in perhaps as soon as just a few days.
The next milestone is ANY closed chord. The closed 3 finger C shape will probably come almost immediately. Getting changes fast and proper muting will take some practice, but the basics will be a matter of minutes. Again, reference Ben's rhythm series.
Next is the four finger G chop. It's gonna take some time, but realize that is normal. Some might get it in a session or two. It took me a few weeks to get comfy with it. I suspect it might take someone with no string background months. Again, reference Ben's rhythm series.
Once you get the above down, you are ready to play some good sounding grass. You will likely have picked up a break or two in the mean time (Ben's cripple creek is easy and fun).