There's another important pain point in the US H1 visa system. New visa applications start in April, but people who get the visa cannot start working till October.

Companies are very risk averse when it comes to sponsoring new works visas due to this. The end result is that typically companies only sponsor new work visas for people that are already working for them(e.g. short term work authorization after getting a US degree, people working at a different branch outside the US, etc).

A lot of people work for large companies outside the US and then transfer to the US. This is not just large software companies, but also Banks, Consumer Goods (e.g. Pepsi, Proctor and Gamble), Industrial Companies (e.g. Siemens, Maersk), Energy Companies, etc.

Not to discourage you, but don't focus a lot of energy trying to get a US work visa unless you have some way of coming to the US and working on a different temporary work authorization. Find a country that where it's easy to get a work visa and build your experience there. Find a large company that is willing to hire you will sponsor a transfer to a country you want to be.

For example, the United Arab Emirates makes it easy to sponsor people for employment visas and there area lot of MNCs in Abu Dhabi and Dubai. Lots of people work in UAE for a few years before migrating to another country. UAE isn't the best place for people who are passionate about software, but you can get a decent job there.