Nafl salaah after the fajr athaan

Mufti Saheb I hope you are well with the permission of Allah, and may Allah keep on using Mufti Saheb for Allah’s Deen . Mufti Saheb I’d like to know if a person can read any nafl salaat after the fajr adhaan is gone? I have a habit of reading 2 rakaats salaatul hajaat before I leave my home every morning. Because of the time of ishraaq been so late(7:05am), the only time I have is before the fajr salaat begins in the masjid. The reason is because I rush off to work straight after fajr n get there jus in time to start working. So my question is can I first read my nafl after the adhaan of fajr is gone and then read my 2 sunnat?