txhope, I am a lifelong Texan, well except for a short and unpleasant stint out west.
Texas social service agencies often contract with private adoption agencies (due to Texas' large population and thus large foster care system) for placement of young children, newborns and toddlers, to expedite the process and reduce bureaucracy when parental rights have been terminated, which often can take years. Meaning a large agency would be in charge of the child's case; these adoptions are categorized as special needs within the agency program and fee structure.
Also in most states, young children are placed in straight foster care homes while their parents are given the opportunity to follow the case plan. If they are not reunited, then these children might be placed with a family member. Often when/if they become eligible for adoption, the family that has fostered them gets the first opportunity. Not many families who have had a babe since birth or toddlerhood are going to opt out of adoption.
Lots of agencies, I think, let you specify gender; however, many do not and more do not if it is your first child. Not sure where you are, but you might contact some private adoption agencies and inquire about state/special needs adoptions (Dallas, Houston, San Antonio) Hope that helps.