Take a look at this post: https://mycomplianceresource.com/forums/topic/e-sign/.
I believe most banks that email disclosures/information have a vendor (i.e. online banking provider or possibly your forms vendor) that sets up electronic verification and maintains record of compliance with e-sign.
Here’s a link to the E-SIGN Act: (7001(c) is where you’ll find the steps you need to take in order to comply.
https://www.bankersonline.com/regs/esign/esign.html#7001