Welcome to the Wefugees community and thank you for your question.
Do you have a legal status in the UK/ are you a UK citizen? Here is a long list of information by the UK government on Living in Germany: https://www.gov.uk/guidance/living-in-germany
If you are looking into moving to Germany and plan on staying for more than three months, you have to register at the local registration office in Germany/ might need a residence permit (depending on your legal status). There are a lot of different kinds that you can have a look at on this Berlin service website: https://service.berlin.de/dienstleistung/325475/en/
Here is more information on entry requirements: https://www.gov.uk/foreign-travel-advice/germany/entry-requirements
As I assume that the mother has sole custody of your child, it is important you talk to her about wanting to be part of your child's life.
I hope this information helps. Feel free to reach out to us again if you need any further assistance!