The thing about Alex being in training before Nick makes sense to me. Alex is about 6 or 7 months younger than Nick, but Alex went into the training when he was supposed to. I felt it was pretty clean Nick had been delayed from going in, and Burt was even worried that if he waited any longer he wouldn't fit in with the others "younger kids" Alex would have went in when he was 13, he did his 3 years of training but had to repeat a year making him 17 when Goldrush started.

As for when the Soldiers would realistically have time to do do their movie thing and go looking for the gold, there was a 4 month period where there was very little progress being made on the mission to hunt Ink. It was totally make sense that after a few month of minimal leads they would have a little bit more free time. Its maybe even around the 3 month mark. Plus their lie of looking for Boulder survivors would be something they would want to do.

I like the story, more of the Soliders is always good. But it makes sense to me, and I really like what little look we get into what the world turned into.