The easiest short-term solution is to work for or intern with a great company in Europe for a while, most likely in London. Your best options are a brand name tech company - Google, Palantir, Microsoft, etc. - well connected start-up - Spotify, GoCardless, Transferwise, etc. - or a technology-driven hedge fund. If you are a really good programmer there will be plenty of people happy to hire you. We have a real shortage of tech talent here. You can always transfer to the US later or get hired at a US company happy to sponsor a visa based on those credentials.

It might be worth talking to some good tech recruiters in London. Depends a bit on your background and how much of your university course you have left.