How long would it take to pick up E-6 in the Army after transferring from the Marines as a SGT and completing SGT Course?

You could be recommended in as fast as a year and pin shortly after. You could spend the next 10 years as a SGT.
Promotions in the Army are based on merit and competition within your MOS at your grade level.

There is a min and a max time. Work hard, learn your duties, focus on training and taking care of your Soldiers and all will be clear. Thank you for your service.

Based upon your prior service, you’ll have the time in service, however You would have to meet the time in grade requirements in order to be boarded. You can attend the board in the secondary zone, however your command will have to approve a time in grade waiver for you. Your official date of rank will be the day you enter active duty Army as a NCO. The AR that covers Enlisted Promotions is AR 600-8-19. I hope this helps. Good luck to you.