Dennis, welcome to TFP!!
A fall build will get it done soon. You won't be able to use the pool this year, but you can open it next spring and have almost immediate use. The places I've worked have always gone on a 6 week wait after backfilling, to let the fill material ~completely settle, before putting the deck down. If you wait all winter to do the deck, you can pour it at your earliest convenience. Some builders charge a little less for late season work. You have a winter, and the freezing to 'age' the pool before you've even dipped a toe in it
A spring build could mean not having the pool until July. You won't have a deck for 6 weeks, which means that while you can use the pool, there is a lot of dirt blowing/ getting tracked into the pool --- MUD! The yard is torn up from equipment so you have to wait until the deck is done to do any planting (not that it isn't w/ a fall build, but snow hides lots of things in the winter). If it's a diving pool, you don't get the board installed for 10 weeks

(6 weeks for the deck to be able to go down and 4 weeks for the deck to cure enough to take the stress of a divingboard). On the plus side, the pool will have been running for 6 weeks and any underground plumbing problems can be solved with a shovel, rather than having to jack-hammer up a section of BRAND NEW deck!
These are just a few quick ideas, in the end - it's up to you to decide.
If you have more questions on what I've said, simply ask.
Good luck with the new pool! You know where to come for any help you need
