This is wrong information you're giving. To obtain legal parental rights in Thailand, a father can legitimize his child through marriage, voluntary agreement, or a court order.
My baby was born 3 weeks ago, cost me 500b to translate my passport and about 15min at the district office. They also gave me the thai and English version of her BC.
Leaving country no need to do 90 day if left before it was due. Your next 90 day will be due 90 days after you return. You will need to submit your tm30 to your local immigration 24hrs after return.