On what basis can a father get full or sole custody of a newborn baby?

There used to be an extreme bias in the justice system against fathers having full custody.  However, over the years, the view of fathers serving a larger parental role have changed.  The family codes in Texas reflect the same attitude and base a decision on custody on "what is in the best interest of the child."

Since the child is a newborn, the natural argument will be that a child should be with the mother for general nuturing and care (like breast feeding) that is more convenient if the child is with the mother most of the time.  However, if the mother is not fit or has issues, then you have a much better shot at getting sole managing conservatorship.  There is not a set list of reasons-- but factors that courts have looked at in the past include:  mother testing positive for controlled substances immediately after birth, number of CPS referrals, number of other children removed from her custody, mom living with an abusive boyfriend.  This is not an exhaustive list-- but it gives you an idea that the court is looking for something that a mother has done to demonstrate that it's not in the child's best interest to be with her.   If she's an otherwise fit parent, then you're going to have issues getting exclusive custody at this point.

You ask a follow-up question though regarding a change in two years.  Even though courts frequently enter "final orders" in custody cases-- they rarely are final.  It is permissible for a non-custodial parent to file a motion to modify custody when situations change.  For example, if she's a good mom now, but then let's an abusive boyfriend move-in next year, then the exposure to abuse would be a material change in circumstances to justify changing custody to you.  The process is similar to filing for custody, but instead is done with a motion to modify rather than an original petition to establish the parent child relationship.