Can you get an ITIN without ever having a US visa?
Short answer
Yes. The ITIN exists for people who are not eligible for a Social Security Number, which covers most non-resident founders. Eligibility rests on having a valid tax reason to deal with the IRS, such as a personal filing obligation from owning a US LLC. Immigration status is not a factor.
What the IRS is checking
A tax reason, not a travel history. Owning a US LLC with a personal reporting obligation or claiming a treaty benefit both qualify. Never having set foot in the US changes nothing.
You may not need one yet
A business bank account runs on the LLC's EIN, not your ITIN. Get the ITIN when a personal obligation or a card application actually calls for it.
Sources
Are you a good fit?
Find out what you would qualify for in the US credit and banking system, in about two minutes.
Find out if you're a good fit →Takes 2 minutes · FreeDisclaimer: This answer is educational, based on hands-on experience helping founders access the US financial system. It is not legal, tax, or financial advice. Rules and issuer policies change. Consult a US-licensed CPA or attorney before acting.