BTDT. Yes, you have to get your SWO pin before anyone will even talk to you for re-des.
As of 2000, you had 18 months from checking aboard to earning your pin. Otherwise, you were a DNQ and the captain had to send a letter to BuPers saying either there was a legit reason (ship in extended overhaul, etc) or there wasn't and you just suck too bad to be a Shoe.
Most guys got it in something between 14-18 mos. Most of what you need in the way of signoffs require you to actually do something or at least observe it - conn the ship to anchoring, conn during flight ops, conn for man-overboards, watch the helo bounce from the tower, etc. Plus you need to get qual'ed as Boat-O, CIC Watch Officer, Engineering Watch Officer (different from EOOW), OOD pierside and OOD underway.
So some of how fast you qual depends on the captain, some on the boat doing the things you need to get signed off. Once you get your pin, your odds of getting picked up for a lat xfer depend on the gaining community's needs.
I lucked out in that my timing was right to get my pin quick (13 mos) and that there happened to be a derth of NFOs.
NOTE: I did all this back in the day of SWOS, then ship. No idea how the timing works nowadays. YMMV.