If you want to go to a specific team and start right away, there's actually a workaround.
Let's say you want to start as HB for the Vikings. Start a CC as the existing Head Coach of the Vikings Start the league so you can adjust your teams roster Trade away any HBs higher than your future HB (I believe a High Draft, Balanced HB starts as 79 OVR) You can also choose to release instead, but I'm not sure if the CPU would try to re-sign him once they regain control, so I would just try to find a decent trade "Retire" as the coach but stay in the league and create your HB. You should now start off as the starting HB for the Vikings
As far as I know, you can jump around to different coaches *before you create your player* and make any roster adjustments you want, just don't advance past the first preseason week until you create your player, and you won't lose out on any XP.
I just did this last night with the Giants. Started a CC as Tom Coughlin, traded Bradshaw to the Chiefs for an MLB and mid round draft pick. Then "retired" as Coughlin (he doesn't actually retire, he stays as the Giants coach) and started up a CC as a Balanced HB. Since I was the highest rated HB, I was made the starter automatically.
You should be able to do this with any team and position, however I don't know if there is a chance that the CPU would try to sign or trade for players who might be better than you. If that happens, I guess you would be pushed back down on the Depth Chart.