The visa for supporting a Thai child (Non-Immigrant O) in the case of unmarried parents requires you to proceed through the Juvenile and Family Court, even if your name is listed as the father on the birth certificate. You must file a petition with the court and then go to your local district office (Amphur) to obtain the Certificate of Child Legitimation (Khor Ror 11). This process may necessitate legal representation and could take around three months. Once the Certificate of Child Legitimation (Khor Ror 11) is acquired, you can submit it along with your application for the Non-Immigrant O (Support Thai Child) visa.
Me (Thai) and my child's father (Foreigner) have not registered their marriage. But we applied for child certification without using a lawyer. By preparing documents to submit to the court myself.
My husband had the same situation as you last month. And I asked immigration. They said it would be fine if it was a holiday. They grant you. This can be done on the next working day, that is Monday and if you go after Monday it will be considered overstay.