Exactly!! If a paternity test was NOT done at birth, and the H signs the birth certificate, it’s all over for him to later argue the child is not his. He is stuck!! Texas knows all about this.
I do believe, however, that some states allow paternity tests against Daddy being the biological Father to seek damages against the twit mother. IMHO, this problem happens faaaar too often, where Daddy is not really bio-Dad.