You can rejoin basically any time you like (a very few dynasties ban new players in the last few days, if it would disrupt the victory condition). Note that several dynasties, especially those based around grinding, are basically impossible to win unless you’ve been there from the start; I’m one of those players who tends to jump in mid-dynasty, though, and have won dynasties like that before, so it’s definitely possible.

If you want to rejoin, make a post or comment asking an admin to unidle you, and you’ll rejoin as soon as they get around to it.

This isn’t the middle of a dynasty.