Understanding startup circuit in this power supply
Correct, Q3 is in the on-state first as it, in combination with D20, is part of a simple linear regulator.  The output of which will be roughly around 24V minus the threshold voltage of Q3.

Q4 is driven by the output of the PWM regulator, U20, through a low pass filter formed by R100 and C19, which is tuned for the switching frequency of U20, 32kHz, and expected PWM duty cycle and keeps the gate voltage on Q4 high enough to keep Q4 on as long as U20 is generating the PWM output.