It's been 5 or 6 years since I did my Trust, so things may have changed. When I did my Trust, I did it through a local FFL that was also a lawyer. Took maybe a week. Then I filed the Form 4 on the can that I purchased. Approval was 8 or 9 months.
So, call it 9 months plus one week for me to have the approved form 4/Stamp and can in hand.
I don't go through the Trust since ATF got rid of the local LEO signoff requirement. Unless you're doing things for Estate planning reasons, there's no need to go through the Trust for new purchases. Just go Form 4.