I live in India, I aspire to work in a product-based company in the United States as a Senior Software Engineer.
There are a couple of approaches that I know of so I will jot them down:
If there is a pathway or any other resources to follow please help.
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.
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.
I've worked colleagues who seem to have done this in two different ways: