Based on studies of muscle protein synthesis, it seems unlikely that a ‘growth switch’ flips on when you got to sleep. More likely, the process of elevated muscle protein synthesis (to repair damage) starts soon after exercise, reaches a peak, and then returns to baseline within 2 to 3 days.
Here is the abstract of one study which examined the pattern of elevated muscle protein synthesis after heavy resistance training:
“It has been shown that muscle protein synthetic rate (MPS) is elevated in humans by 50% at 4 hrs following a bout of heavy resistance training, and by 109% at 24 hrs following training. This study further examined the time course for elevated muscle protein synthesis by examining its rate at 36 hrs following a training session. Six healthy young men performed 12 sets of 6- to 12-RM elbow flexion exercises with one arm while the opposite arm served as a control. MPS was calculated from the in vivo rate of incorporation of L-[1,2-13C2] leucine into biceps brachii of both arms using the primed constant infusion technique over 11 hrs. At an average time of 36 hrs postexercise, MPS in the exercised arm had returned to within 14% of the control arm value, the difference being nonsignificant. It is concluded that following a bout of heavy resistance training, MPS increases rapidly, is more than double at 24 hrs, and thereafter declines rapidly so that at 36 hrs it has almost returned to baseline.”
Here is the reference: https://pubmed.ncbi.nlm.nih.gov/8563679/
I’m sure you can more stuff like this if you start searching the academic literature.