The short answer is NO. However, the startup must be operational. It must have some money and make money to pay the salary of its H-1B applicants. It does not have to be profitable. As we know, even huge companies like Uber and Snap are not always profitable, but they definitely file for a bunch of H-1Bs and get approved.
In general, NO. You cannot own an entity that sponsors you for an H-1B. Even if you have investors that have partial ownership of your startup, there is still an issue with filing an H-1B for yourself. HOWEVER, if you have investors and co-founders that own more than 50% of your company and your startup is structured so that your co-founders and/or your investors can hold you accountable for poor performance–be able to fire you, lower/raise your salary, etc.--then you may be able to pull off an H-1B for yourself.
Generally, YES. As we’ve seen, you yourself cannot technically perform services for your own startup. However, if all the requirements of an H-1B visa are met, you can file H-1Bs for your existing and potential workers, and you can sponsor them for green cards as well.
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