Thanks for reaching out to the wefugees-community!
The vocational trainigs (Ausbildung) to become a nurse usually start in September or October of each year. There are also a few programs that start in different months even still in 2020. You would need to search the web for those offers for example here at https://jobboerse.arbeitsagentur.de/vamJB/startseite.html?aa=1&m=1&kgr=as&vorschlagsfunktionaktiv=true. Otherwise you would need to start applying now in order to get a place for the end of next year.
I hope my answers were helpful and I would be very happy if you would contact me again with further questions. I'm a consultant with mbeon and I‘ll be glad to help you over a longer period of time. Mbeon is an online advice for migrants via the mbeon app, which you can install on your smartphone for free. Download it from App Store or Google Play Store. You can find me in the mbeon app under my Name "Frau Rukundo" and get confidential individual advice in a secure virtual space without other people reading our conversation. Further information: www.mbeon.de.