You used two different terms: "abandoned custody" and "full custody".
I am assuming that when you said "full custody" what you meant was how soon you could file a suit to be named "sole managing conservator". The sole managing conservator of a child is the person who gets to make all the important decisions about the child's residence, care and education. You can file a Suit Affecting the Parent Child Relationship to seek this at any time - your girlfriend doesn't have to have been gone for any set amount of time before you file. If you are successful, your girlfriend would likely be designated a "possessory conservator". This would mean that she would be entitled to visitation with the child at certain times but no real decision-making authority. If she is not involved in the child's care and is providing no support you have a good argument for being named sole managing conservator.
If, by using the word "abandoned", you were talking about terminating your girlfriend's parental rights entirely, the Family Code does impose rules on when that kind of a suit can be filed. Sec. 161.001 of the Family Code provides the different grounds for a termination, with the most relevant to your situation seeming to be:
1. If your girlfriend voluntarily left the child alone or in the possession of another without providing adequate support of the child and remained away for a period of at least six months; or
2.If your girlfriend failed to support the child in accordance with her ability for a period of one year ending within six months of the date of the filing of the petition.
Also, a termination suit is considered a drastic step and the court will impose a higher burden of proof on you than if you were simply seeking to be named a sole managing conservator.