If you get on a northbound Green or Yellow line train, you can transfer at Pioneer Square. From where you are starting, it looks as though the nearest station would be SW 6th/Madison. This means you would board, then get off at the next stop to transfer. This would save you roughly 4 blocks of walking. It may actually be faster to walk, especially at that hour of the morning when trains run less often. In fact by waiting for a Green/Yellow train you may actually miss a Red Line train.

My suggestion would be to go to the SW 6th/Madison station, since it's essentially "on the way." Buy your ticket, and check out the digital message sign which indicates when the next train is arriving. If it's more than a 5 minute wait, then just walk up to Pioneer Square.

(If you board a Green Line train, you can also wait until you cross the river and transfer anywhere from Rose Quarter to Gateway stations...the only advantage to that is that you get a same-platform transfer, whereas at Pioneer Square you have to walk around the corner. Here's a map.)

(If there's a northbound Green/Yellow train just pulling up to the station as you arrive, don't worry about buying a ticket since you're in the free rail zone...you can just wait until you get to Pioneer Square to buy the ticket...but make sure you do get one before you board the Red Line because they have been stepping up fare inspections.)