Bangladesh was established as the country we know now in 1971, i.e. yesterday, when it got its independence from Pakistan, which it was part of since 1947 after the Partition of India in that year.
I think here is a fantastic example of the fluidity of identity; the past 61 years, the people who lived in the area have called themselves Indian, Pakistani, Eastern Pakistani, and Bangladeshi. 61 years. One person’s ¾ of a life… Wow! And why do we worry about nation states exactly?