Married Father vs Suicidal Mother

My question involves a child custody case from the State of: Texas

My fiance is from Texas, as is his ex girlfriend, who recently contacted him saying that he is the father of her two year old son.

We're both military and soon to be married. She is suicidal and living with her brother and has no job.

Would we win in a custody battle?

Married Father vs Suicidal Mother