In terms of returning to the US, you can enter and look at applying for jobs while you're there (meet people, have interviews etc) but you'll still need to go through the H1B procedure, which typically takes 6-8 weeks.
The visa waiver program (VWP) means you can be in the US as a tourist for up to 90 days at a time, with only 180 days in total in any one year period (* I'm 99% sure it's any one year period, though might be worth double checking). So the likelyhood is even if your in the US for that time you'll have to leave before the paperwork goes through. Immigration can get a bit funny though, so don't bank on being able to make loads of trips (they like you "out" as much as you're "in")
Now a word of warning. As a recent grad trying to convince US employers to H1B you and bring you over is hard. You're in a better position than 99.999% of the population though - math and machine learning is hot in any company. The issue the company has to decide is, "Is it worth us spending the money and time trying to get an H1B for this guy, or none of the hassel for a 'home grown' employee". If they can get your for 1-2 years it may well be, and experience with your previous company is a big plus.
Finally, trying to get interviews from the UK to the US is very tough. I wouldn't recommend applying for job boards, but look at contacting CTOs tech leads directly. Maybe my case is unique, but I applied to about 150 job board postings over about 3 months for a jobs in the US. I have an undergrad from Oxford (biochem) and masters in CS from Imperial London (GPA 3.7/4.0 respectively) and I heard nada from anyone except literally the first add I applied to. However, I've had quite a few interviews through just emailing people, so it is possible.
If you want any more info feel free to contact me (through the various means on my HN profile). For the record, I was in a VERY similar situation to you in terms of the US/UK issues.
[EDIT: Sorry, I totally projected that you're actually from the UK because of your English and what you said about moving there. I think everything still stands though, assuming your country participates in the VWP?]
As a recent grad trying to convince US employers to H1B you and bring you over is hard.
No doubt. I feel very, very bad for the OP, but I am a little surprised at this:
I refused opportunities with Google, Bing, and two startups. I told all those people I wasn’t able to consider any offer, since I had already accepted one (so I thought).
If the OP had done all the required research (and it certainly looks that way), it must have been clear that the H1-B is nothing to mess with. Turning down opportunities until you have the visa in your hand and you've gone through customs sounds crazy to me.
Getting a visa is very hard. It's not Google/Microsoft's first time at that rodeo. Even better, big companies don't change their minds in a hurry. The startup was always much riskier. Funding might change, a new better candidate might appear, the whole company might pivot away from your skillset.
I realize its easy to point out flaws from the safety of my desk chair, and I have nothing but sympathy for the OP. I've been there when I had to leave the US the first time after my studies ended, and it's really hard. But that experience has what bred my heathy paranoia for these things. Always take the safer bet.
Sure - I had sort of assumed those offers were for non-US locations though? I've been approached by a number of [american] companies and recruiters for jobs in London.
I'd be really interested to hear about the H1B from the employers' perspective; there must be some HN members who've engaged in the process?
The visa waiver program (VWP) means you can be in the US as a tourist for up to 90 days at a time, with only 180 days in total in any one year period (* I'm 99% sure it's any one year period, though might be worth double checking). So the likelyhood is even if your in the US for that time you'll have to leave before the paperwork goes through. Immigration can get a bit funny though, so don't bank on being able to make loads of trips (they like you "out" as much as you're "in")
Now a word of warning. As a recent grad trying to convince US employers to H1B you and bring you over is hard. You're in a better position than 99.999% of the population though - math and machine learning is hot in any company. The issue the company has to decide is, "Is it worth us spending the money and time trying to get an H1B for this guy, or none of the hassel for a 'home grown' employee". If they can get your for 1-2 years it may well be, and experience with your previous company is a big plus.
Finally, trying to get interviews from the UK to the US is very tough. I wouldn't recommend applying for job boards, but look at contacting CTOs tech leads directly. Maybe my case is unique, but I applied to about 150 job board postings over about 3 months for a jobs in the US. I have an undergrad from Oxford (biochem) and masters in CS from Imperial London (GPA 3.7/4.0 respectively) and I heard nada from anyone except literally the first add I applied to. However, I've had quite a few interviews through just emailing people, so it is possible.
If you want any more info feel free to contact me (through the various means on my HN profile). For the record, I was in a VERY similar situation to you in terms of the US/UK issues.
[EDIT: Sorry, I totally projected that you're actually from the UK because of your English and what you said about moving there. I think everything still stands though, assuming your country participates in the VWP?]