Welcome back to the Wefugees Community and thank you for reaching out to us again.
I remember from your last post, that you are married to a German woman. As you explain above, your child was born after you got married. This means that you are automatically recognised as father of the child and explains why you are also registered in its birth certificate. The acknowledgement of the paternity and the declaration of custody only needs to be done if the parents are not married.
Regarding the visa procedure, I can not give you any prediction about the time frame and I am not sure if one visa will be faster to obtain than the other type. However, I would recommend you to clearly explain about your life context in your visa application. Highlight that you have a child in Germany you can not be separated from for a longer period. The pre-approval letter ("Vorabzustimmung") of the immigration office is giving you the advantage, that the German embassy does not need to wait for the immigration office's approval anymore (which usually takes a considerable amount of time). You can apply for an appointment at the German embassy in Ghana and only fly out shortly before the respective date. Please also check the exchange in this thread for more information.
I hope this helps and don't hesitate to get back to us with any further questions.
All the best,