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Dear Ms. Robinson,
Thank you for posting your request on History Hub!
Because of a 72-year restriction on access to the Census, the most recent year available at the National Archives is 1940. The 1950 Census will be released in 2022; and the 1960 Census will be released in 2032 which would be the census that your mother would recorded in.
However, most states will provide a birth certificate if your mother can obtain witness statements from relatives, use family bibles and baptismal records, or provide documentation about her birth from hospital records. We suggest that you search the website of your state’s vital statistics office to ascertain how to apply for a birth certificate using the documents noted above. You also may wish to review Need a New Passport & Don’t Have an Original Birth Certificate?
We hope this is helpful. Best of luck with your family research!