Conditions for the validity of Salaah

Performing the sunnah salaah once the salaah time enters

Q: In Ssaudi the Adhaan is given at the very moment the salah time enters. In India, except for maghrib, there is a delay in the Adhaan being given for all the other 4 salah. The delay varies from places. Suppose Bangalore Asr time sets in at 4.04 pm but Adhaan is called at 4.30 and jamaat starts at 4.45 pm.

My question is, should the sunnah be offered after Adhaan or can one offer the sunnah once the time of the salah enters even before the Adhaan is called out?