To clarify a couple of things. No, the character never needs to take part in an actual plot to be part of the canon. If you submit your character in the character submissions forum, and they're approved, they're canon, whether or not they ever actually join a plot. However, solo RPs aren't guaranteed a place in the canon in the same way plots are, so while the character might be, what you do outside of the plots might not be.
Now, that said. You don't need to wait for a plot to be starting to join a plot. Most GMs are more than happy to work with you to find a way to bring your character into their plot somehow, and just pick you up either in between chapters/missions/episodes/etc, or in between threads at the very least. Sometimes you can even be pulled in in the middle of the thread. So don't worry about that, and just look around and see if something catches your eye. If it does, go talk to the GM for that plot, and see what they say.
And, all that out of the way, Welcome to SARP!