Is it possible to get on a PC for your 1st tour?
No. Pretty sure same applies to LCS.
To put it bluntly, with only 3 1110's assigned, one of whom is the CO, they don't have the space for deadweight nonquals.
Coming out of a first tour, the expectations are that you OJT to pick up the basics: learn how to drive and navigate a ship, basic engineering, DivO admin/maintenance, and general non-specific warfare stuff.
And generally speaking, smaller ships offer better opportunities to get good at those fundamentals, because you have less bodies competing for driving time, and less emphasis on "specific combat stuff".
The best thing you can do with your first tour, IMO, is to just focus on SWO and EOOW. Once you've paid those dues, have fun with your 2nd tour.
And you can seriously go off the deep end with your 2nd tour: I know a guy who got picked up for NGLO his 2nd tour and worked as a JTAC with MARSOC.