Bangladesh independent from the start

How could Bangladesh (probably would be called ITTL East Bengal or just Bengal) be independent from the start in 1947, and be an Islamic Republic like Pakistan?
 
I don’t really see it being called Bengal, as that implies that it has control over West Bengal.

I also don’t see it becoming independent, as another Muslim-majority country kind of destroys the entire two-nations theory upon which India was partitioned.
 
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