I feel giving around 3.000 - 5.000 is a bit low. I guess it could be "kinda" ok if growing up on the Thai country side and grandparents take care of the child while the girlfriend works in some nearby farms, in the factory or in the city. Still, for the child I doubt it'll be a nice existence.
I'd say pay at least 10.000 a month for a child. Sure, 10.000 THB is about the average monthly wage here on the country side, but if it's your biological child, surely you'd want the child to be in a somewhat better position, right?
Better still would be to try to take custody of your own child, if your girlfriend can agree on that. You can make sure the child gets decent education and such. Can get a nanny to help take care, etc... More expensive surely, but imo better.
Best is if the child has good contact with both biological parents and both parents can get along well and both take care of the child, but I am sure that is out of the picture. There's been research done on children that are missing one of the most important figures in their lives (father figure / mother figure) and generally it can cause issues when the child grows up.
As a father it's also possible to get a dependent visa, so that can make staying in Thailand long term easier.