There's no technological barrier to starting it now we have all the capabilities, there's only a financial constraint.

SpaceX has significantly reduced lift cost into space but it would indeed cost trillions. Current lift capacity isn't saturated but they would definitely need the additional capacity of their next gen rocket to service it and then multiples of those. Unless Boeing and Blue Origin get their shit together.

Lift capacity becomes less critical if metals mining and refining in the asteroids gets up and running, then you can much less expensively move material from asteroids to the space hotel. That's def decades away though, there's tech issues with that still unresolved

TL;DR start project in 2027 ? Sure if they can find the money, definitely take decades to finish with currently planned lift capacity though. Needs asteroid mining to be viable