Hmm, its an interesting question for me, overall I'd say no, but part of that is down to lifestyle and choices in the last 7 years being here.
Before I moved, I'd travelled a lot, lived abroad at uni and then lived in London for 11 years (I'm not from there so was nowhere near family in the UK)
I moved here with my work (used to work for a US company in the UK and landed a job here) and the culture was very very different in the office. I knew people at work but they weren't friends when I moved over, and I knew only 1 person outside of work, and that was a friend of a friend
I had massive culture shock (to be expected I think no matter where you go) and it sounds really quite stupid now, but I expected there to be more similarities with the UK than I have found. I have no idea why,. Altho it's English, the use of language is totally different, different intonations, different meanings, gestures, body language etc which in someways has made fitting in harder than if I didn't speak the language at all.
I was single and in my 30's when I moved over and found starting from scratch with my social life etc really hard tbh. I wouldn't necessarily solely attribute this to the US / NYC but I think its harder the older you get.
Fast forward to now and life has changed again as I married a local and we have a kid - so our lifestyle has changed and we're currently in the quandary about staying in the US versus the UK due to schools, guns, politics, being closer to my family etc.
The challenge now is I've been away long enough to feel like a stranger in the UK too and realize its not without its own challenges either - so nowhere really feels like home!
My only advice is to take it one day at a time - accept there'll be days when you think "wtf did we move?!" and push yourselves to do stuff socially that you wouldn't normally - there's a ton of good meet up groups in the city for like minded people and NYC is great for kidless people as there's so much to do. If you get homesick for proper English foodstuffs (I predict you'll find yourselves craving shit you'd never touch at home!) there's a great place called Meyers of Keswick in NYC where you can get all your pie and biscuit needs!
If you need help or info just shout [grin}