I recently received my ITIN and applied for a Chase card, even though none of my existing Amex or HSBC accounts were linked to my ITIN.
Initially, I kept getting declined, but I continued calling Chase until I finally reached a representative who was genuinely willing to help. They asked me a few verification questions, processed the application, and sent me a link to upload supporting documents. A few days later, my application was approved.
Based on my experience, I don't think you necessarily need an established U.S. credit history to get approved for a Chase card. Persistence seems to make a big difference.
The same thing happened to a friend of mine. His first application was declined, and after several calls he still couldn't get it approved. About a week later, he applied again, was initially told it was declined, but he kept following up and eventually found a representative who reviewed the application properly and got it approved.
So my advice would be: don't give up after the first decline. Keep calling, ask for a manual review, and if needed, submit any supporting documents they request. It worked for both of us.