To unlock the SVT-40 in Call of Duty: WW2 you have to level up the infantry division all the way to the end of level 4. The way that you level up the infantry division is to use it in one of your classes during matches. Then enter the headquarters and go see the division prestige guy. Select the infantry division and proceed with the prestige.
This unlocks the SVT-40 no matter what your soldier level is.