In my experience it usually takes 2 weeks for a skill to pop. Have been playing for about 3 months though so other GMs with more experience can verify this
I train 5 players (each getting 48+ minutes) at 2 positions with a level 4 trainer. My players usually are 18-20 with potential of 7 at least
Its unusal for a player on my team to pop after 1 week, it happens but not enough, especially if the skill is high