Dhaka is often said to be around 400 years old, but a more appropriate statement is that Dhaka became a Mughal capital around 400 years ago. The city's history dates back to the pre-Mughal era. 

Want some proof? 

Binat Bibi's Mosque or the Mosque of Bakht Binat at Narinda was established around 1456 CE, during the reign of Sultan Nasiruddin Mahmud Shah.

Although the building has undergone hefty renovations and alterations, this mosque bears the testament of a pre-Mughal Dhaka. It points to the fact that the advent of Islam in Dhaka started before the Mughals took authority. 

It may also be inspiring or interesting to some that the oldest surviving Dhaka mosque is named after a woman. The identity of this woman is shrouded in mystery. According to an inscription, she was the "daughter of Marhamat". 

Sources: Muslim Architecture in Bengal by Ahmad Hasan Dani; Notes on the Antiquities of Dacca by Sayid Aulad Hasan; Banglapedia.