Stupid question but you don’t mention , I’m just assuming you do already have a driving license in your own country ? Because you do need one even if your going down the agent route
I can’t imagine any immigration office will do that .. I had a friend here ( Pattaya ) went 16 days before the end date of he’s 45 days , and was told to come back nearer the date 🤷🏽
Others , it’s that time of year ( other than the past couple of years ) this is to be expected … couple of hours not the end of the world , get your ticket , go get a coffee etc ..