I've only been playing the game since December, but I've already taken a team from 4th to 1st:
http://www.whatifsports.com/HBD/Pages/Popups/FranchiseProfile.aspx?fid=5069
There wasn't any talent in the pipeline here; the previous owner didn't even bother to sign his draft picks (worse, hedidn't even make an offer, so I didn't get any comp picks). All I did was move to a pitchers' park where my durable but mediocre starters could thrive, sign a couple bargain-priced sluggers, and make sure to play my best defenders.
Admittedly, this is isn't a top-tier league. But if a rookie like me could do this, I'm pretty sure anyone can.