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I mean, (when they're hiring) all the big techs are hiring from wherever they can. Local is great, across the country is great, outside the country is fine too. Really big tech can do stuff like hire you, have you work near where you are or somewhere that's easy to get visas for, and sponsor you to apply for H-1B when the lottery opens every year until you win or they can apply under another category (I think there's a category for 'important overseas manager' which sometimes they'll do). Then once you're here, I think it's relatively straightforward to get on the path to a greencard, if the employee wants to sponsor that.

Getting directly hired seems hard; H-1B requires application by early April and if you win the lottery, you can't start until October. I'm not sure many employers will be willing to do that. Maybe if you can WFH in the meantime? Other work visas might not have the same application -> start times, but are still a bit of a random wait on immigration processing, which could be denied.

Getting a masters in the US is a good pathway to immigration though, yes. You can work under OPT after graduation, and you have time to mingle and maybe find a spousal sponsor ;) But it's probably too late for that.

I got in the easy way, through birth, so I don't have direct experience. But I wouldn't suggest you rule it out for sure. I think there's also a 'diversity visa' you can apply for, and they might draw your name out of a hat. I know someone who got in that way. But I know a lot of immigrants because I worked at big tech companies, and they're a magnet for immigrants.