@Cr***
, you can get that 60 day visit thai family extension on a 30 day visa exempt entry too.
I don't believe you can get the long term extension just by getting married after the child is born.
I think by then you're too late and with need to go thru family court to be recognized as the legal father.
In order to get the long term extension you need to be the legal father and you need to show 400K baht in a thai bank account in your name only or a letter from your consulate stating you get over 40K baht a month in income from abroad along with the required documentation.
If your child's thai mother is agreeable to the process of going thru family court it takes about 6 months all in to get thru the process and get granted parental rights.