This depends on which masjid you believe is calling the Athan on time. A lot of masjids call the Athan few minutes before the real time so that people would stop eating in Ramadan. This is wrong because if people pray, their pray would be invalid because it was done before the proper time.

Therefore, I suggest that you don’t pray the Sunnah until the last one calls for Fajr.

And Allah knows best

I hear the Adhaan of several Masjids but the Masjid that I go gives Adhaan 2-3 minutes later to all the Masjids. I usually go before the Adhaan to the Masjid I attend so if I reach the Masjid before the Fajr Adhaan can I pray the Sunnah as I heard the other Masjid’s Adhaan? or I should wait for the Masjid which I attend to give Adhaan then proceed.