iRule with monitor (monitoring if connection = first)

BigIP will do this out of the box with session persistence. Choose from IP, Cookie or if you're feeling adventurous you can design the persistence method yourself with an iRule.

Determining whether the connection is a new session or a new connection for the existing session is reasonably protocol dependent (Except where you do something like assume a 1:1 relationship between IP and client and persist at the source IP level of course)