How to get a job abroad without studying in a university?

One option is getting a job within India for a company that has offices in the United States and internal mobility for engineers to be transferred from India to the U.S. with sponsorship. You would have to join and make an impact. In that process, it would be good to talk to engineers at the company on how they made the transition, if you can find some who did. You could also get counsel from HR or your manager.

You will have to be gentle with this though. Do not interview asking about this or come in on day 1 asking how to transfer. First, prove yourself. Then, explore that opportunity.

I've worked colleagues who seem to have done this in two different ways:

1. Like David said, via internal transfer. Join a multinational company with good internal mobility and find a job via internal transfer at some point. Internal transfers are usually preferred over external hires for the big tech teams generally, so once in, you potentially have an advantage even compared to an external hire from the US. I've known multiple engineers who've used this path to come to the US from India in both Amazon and Google.
2. Do a tech-centric degree in an American University. This takes way longer, is way costlier $$ wise, but I've also seen many folks pursue this path because this enters you into the US talent pool post graduation.

It's absolutely worth building a personal brand around both open source contributions and LinkedIn. It will take time to develop though, so I'd combine that with David's suggestion.

Getting started in simple though, just start writing and sharing what you are learning or contributing to.