You have to interact directly with the other character to invite them, and since you can't be logged in with multiple alts from the same account at the same time, that means you can't invite your alts. However, it is possible to ask someone to join just briefly, long enough to help you establish the FC and then wait while you log out and in again on your alt(s) so they can invite all your alts into the FC for you. (Just make sure you give them invite rights. I can't remember whether that's a default or not.)

(People on the 14-day free trial program can't join an FC or help to establish one.)