As you know carrier pull-in is required to get the estimate of the carrier frequency, to start the PLL, in real time GPS, this is done through FLL, but in soft receivers it is done similar to acquisition.

usually it is done using large data (4 ~ 20 ms) to minimize or filter out the noise.

A PLL requires better estimate of frequency than provided by the usual acquisition phase, and that is why pull-in is necessary.

After acquiring the GPS satellite by locating its frequency you need to track continuously this frequency which varies with time due to Doppler shift. The local oscillator has also phase noise and frequency drift. Successful detection requires coherency between the received carrier and the locally generated carriers. The phase locked loop performs this task it synchronizes the received carrier and the locally generated carrier. While the delay locked loop synchronizes the locally generated pn code to the received code.

The acquisition phase in the PLL is required to pull in the PLL to the so called lock-in state irrespective of the initial frequency difference between the locally generated carrier and the input carrier to the PLL. The lock in state is that stae where the frequency difference can be automatically zeroed.

In starting the reception after the satellites acquisition phase you can not grantee that the frequency difference is smaller or equal to the lock in state. An engineer goes always to the sure operation.

You can see an implementation of the receiver in the paper:https://www.researchgate.net/publication/236217926_Implementation_of_a_Complete_GPS_Receiver_on_the_C6713_DSP_through_Simulink_Receiver

Best wishes