Amar started his acting career during college in 1995, making his professional debut in an English play titled "Carry On Professor".

During the early years of his theatrical career he acted in plays speaking in multiple languages including English, Marathi, Gujarati, Hindi and Urdu.

Over the next three years, Amar appeared in plays such as Maa Retire Hoti Hai, Dr. Mukta, Pati, Patni Aur Mein.

Babaria's first acting role was in a Hindi play titled Maa Retire Hoti Hai[4] with Jaya Bachchan.

Finally, in 2001, Amar acted in another Hindi play called Pati, Patni Aur Mein[5] with Shatrughan Sinha.