Can a TIME_WAIT connection be restored?

Is it possible to restore a connection that is in state TIME_WAIT?

If not, I use raw packets (forgering the source), is it possible?

(Please understand that I do not intend to do bad things, it's just a matter of curiosity)

No, this is not possible. TIME_WAIT is a state that acts like a bucket to catch packets that could belong to the closed connection and could screw up a new connection using the same IP/Port combinations. This is an error-catching state. Replaying packets from the original connection will be sent to the bit-bucket and not interfere with any other connections that may exist.