The Vine City Marta Station on Northside Dr is the closest Marta station to the Ga Dome. The worst crowd problem, by far, is at the Dome/CWCC/Philips Arena/CNN Center Station.
Here is what Marta has to say about that:
"The Georgia Dome is located at 1 Georgia Dome Drive NW, in between theDome/GWCC/Philips Arena Station and the Vine City Station on the blue/green rail line that runs east and west through Atlanta.
The Vine City stop will have less traffic and put you more easily on street level near the Dome, while the Dome Station has a direct entrance into the building on a lower level."