At this point, I think there are two potential timelines remaining for a team in Phoenix: the Mat Ishbia timeline, which is "two years after he decides he wants a team", and the anyone else timeline, which is "how long will it take you to buy land, get it zoned properly, construct an arena, and build out an arena management and hockey ops structure"?
The Ishbia plan is the same pathway Ryan Smith would have had for an expansion team, where you give yourself lead time to build up hockey ops and figure out where you can incorporate tasks into the Suns ops structure, then do branding work and have an expansion draft. This probably coincides, if it ever happens, with Ishbia deciding he wants either a new arena or a heavy renovation of Footprint, and wants extra leverage to get public support behind him. This means Phoenix is team #34, most likely, after Atlanta.
The other plan, well, that's the nebulous one, and that version pushes Phoenix out to #35 or 36 back into the league at the earliest. If they take their time and do it right, though, this one could pay huge dividends, putting the team into the hands of an ownership group who wants them for the sake of owning a hockey team, not for the sake of having a second tenant to fill dates in their big brother's arena.