Tactical error No 1.
You went by yourself, send the good lady, with the baby, don't feed baby until after the account is set up.
Suddenly the teller, [who isn't planning on having kids for the next forty or fifty years] will do anything to get the unaccustomed noise out of the building.
here is a blank application, just sign and I will fill it out for you stage.
You can spend the time [only the short minutes though] entertaining little miss with an ice cream or similar spready thing, then have to rush back to the office as soon as the good lady comes out of the bank.
That sounds like a splendid way to organise it! Next visit, that's the strategy!!
If it is a male counter jumper, and the good lady is up for it, a bust in the mouth of the squalling babe has a similar effect.
Speed, get rid of what I want to look at but can't.