They could simply call your previous supervisors to check the employment history. If your previous employer is out of business, you'll need to submit copies of past W2 to verify employment history.

That's the policy at my company, and I had 4 years of work experience. I think you'll be fine, don't worry much. If you're recently approved for DACA, the background check and SSN verification might be a hassle. But in the end, you'll be fine.

I was nervous when I applied for a new job after receiving DACA work permit, but everything went smooth. However, the background check delays the process for 1 week; the background company cannot verify my SSN. I had to fax in a copy of my SSN card to speed up the process.

What position at the bank are you applying to ? Depending on the level of your position, the background check could get very meticulous.