lightning fast, if possible

You should contact the Alliance leader, or one of its members, and convince them you belong to them.

The fastest way to receive an alliance invitation is probably by knowing what you want and working for it. You don't know what you want, you don't apply for the right alliance. You don't know what you want, you don't know your role - and if YOU don't know your role, how can you convince an alliance you are the right man/woman for the job?

So the fastest way is to be very efficient at ''making yourself'', i.e. creating a role. Now, as for how that may take years...that's another talk, isn't it?