Only in extreme circumstances. If they start 30 minutes early, enforcement will just tell you it's no big deal. But you lost a significant part of your sleep time. And there's the whole deal about police brutality in the US making that a potentially problematic solution.
With that said, often it's not even an option. See: NYC where overnight construction variances are approved left and right. In our case, a construction project that is breaking all the rules and even got brought up in court is still going. The city won't (and even the court) won't do anything because "need more housing, at all costs!"
All in all it doesn't matter though: even if everything is done by the book, it gives you a strict 8 hours window to sleep. Not one minute after, not one minute before. That's my point. The rules already give you zero options unless you're straight up lucky.
Most people have some choice about where they live - noise should be a factor when deciding where to live. In a place as busy as NYC, I would think a person choosing to live there places "quietness" low on the list of priorities.
First, not really: moving means leaving your job (unless you can do it remote), and incurs significant monetary expenses. If you have a family it's even worse, switching school, etc.
Even if you do get to pick where you live, we live in a highly dynamic world. The quiet dead-end of today could change within a matter of months and have a highrise on it, especially given how cities are sometimes taking drastic actions to fight the housing crisis.
Finally, there's a difference between ambient noise and outliers. You can live on Manhattan and be naturally dealing with cars and people, but then your upstairs neighbor decides to get into drumming or start dating someone with 3 toddlers, and that's a whole different game.
Even if we take out changes from the equation, it's VERY hard to properly assess how noisy somewhere will be, even if you visit it multiple times. By the time you realize there's a problem, you're stuck with a mortgage or a lease and have to deal with it for a year or more.
In France after lockdown, bars and people can be noisy up until 4am with no code enforcement whatsoever. In Paris intra muros: https://youtu.be/GaYPLv6diXA
