FT Recruiting Process as a SA

Currently doing my SA stint at a regional MM coverage group, and although I’ve been doing well and learning a lot, I don’t find the industry to be interesting and the group is a bit too small for what I’m looking for. That being said, I’m looking to recruit FT at a stronger group, but it seems that the process is a bit tricky. How / when do I go about networking for FT opportunities, and is it safe to be doing that while still being a SA and awaiting a return offer? Also, curious to hear thoughts on how the FT recruiting landscape will look late into summer and early fall, and if I can reasonably expect there to be other opportunities? Any clarity or similar experiences are appreciated.