Going from uni in ldn to working in the USA

Hey everyone, currently about to apply to uni in the uk for 2027 entry for maths related courses, my top 3 choices r defo oxford imperial and Warwick, and I think imperial is within grasp but Oxford is always a gamble.
Wanna ask for the potential of working in the US with a UK educational background? I’ve recently started considering this more and more since london has j become so grey to me tbh, and I’ve always loved the idea of working in nyc for a bit for at least a year in my life.
What does this process normally look like? I’d guess there’s 2 main ways - u apply to us jobs with ur uk degree, or u apply for london based jobs and get moved into offices in the US? Pls someone correct me if im wrong lol
On a side note - is it true the only respected uk unis in the eyes of the US are Oxbridge? Wld imperial not be well respected enough from a US employer’s eyes?