I successfully opened a Chinese bank account without residence permit more than 2 years ago with China Construction Bank at a branch in Shenzhen. All I needed was a Chinese phone number and my US passport. After the account was open, I was able to get it linked up with WeChat, after going back to the branch and getting some help about the name on the account. For me it was, last name, first name, middle name all in caps. However, I went back a few months later to add online banking and was told they couldn't change my account. Adding online banking would essentially be making a new account and their requirements had changed and residence permit was required. My existing account was left untouched and still works to this day. If you have a few hours to burn and a translator to help, you can certainly try a few different banks and see if you can get an account.

The other alternative is to get a US issued credit card that works with Union Pay. A quick google search shows ICBC in the US has been offering these -- ICBC Union Pay Cards. However, not sure it will work as expected. There's a long discussion here on flyerTalk.