I did note your other posting in Tarrant Co.
It is unlikely you'll find a birth certificate for her. Texas did not require BC's until 1903 and it took decades for the counties to comply. Her becoming an "orphan" may have been due to a multitude of potential reasons. An "adoptive" birth certificate may not have been produced. Original BC's are not "destroyed," but placed under court ordered secrecy ... IF there was such at that time.