Will Birth Certificate issued after 1year of birth work for GC?

I have a birth certificate issued after 13years of my birth. I was born on 1977 at home in Jorhat Assam. In this situation can I get non-availability of birth certificate from the municipal health department? If not what are the options I have?

You can get NABC from municipality if they are ready to issue it

Do you know if anybody / agency can help on this while I am in US?