To be honest pal, I rarely train them up during an off-season, I find it very time-consuming with little improvement. All I have done is win, win, win.
At the beginning of his career, Baumjohann probably isn't good enough to go into a good team such as Liverpool like I chose. In the first season give him regular substitute appearances for half-an-hour or so, when your team is winning or going to win.
He improves very quickly straightaway, and then over the next few years he improves a bit more gradually. I had him as a regular first-teamer from the half way point of season 2. The picture I posted above are his stats midway through season 4.
These methods I use aren't just for Baumjohann, I do it for all young players and I suggest you do the same. Just give young players regular chances to break through, despite below average stats, and I assure you they will come good after a few league triumphs.