This can be done as soon as you gonna enter Personnel module.
Go to Administration Wing and you'll see "Happy Obsolescence Day, Tacoma Crew" written on a wall with yellow letters behind the big table.
To get an trophy you gonna need to find all missing letters for this sign in this area.
There are "O" and "E" just below the sign on the floor.
Another "O" is in the Lavatory room near the table.
"M" is on the floor of the lower area.
Just collect those letters one by one and attach them to a wall.