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How to get a job in Silicon Valley startup as a non-US citizen, without having a company sponsor?

Unfortunately, there are not a lot of options for a person in your position. If you are able, you can work for a multinational company abroad for one year and then come in under the L1 intra-company transfer visa. Or you can start up a company abroad and also come in under the L1 intra-company transfer visa to open up a new office here. If you have substantial capital, you can try to come in under the E visa to start up a business here. There might be some green card options available to you that don’t require an employer, but those unfortunately have strict requirements.