Are there specific verses or supplications, such as reciting Surat Al-Baqarah for 40 consecutive nights, that help a girl get married?

There are no specific surahs or supplications for expediting marriage, but it is recommended to have piety towards Allah and to be persistent in supplication, especially during times when prayers are answered, such as the time before dawn (sahar), between the adhan and iqamah, and after Asr on Friday.