Yes, it is possible to register your child in a day care centre.
You can contact the family office, which will be happy to help you with registration and finding a daycare centre. You don't need an appointment and can just drop by.
The Family Office is at Junkerstraße 1 48153 in Münster and is open from Monday to Friday from 09:00 am -12:00 pm.
You can also come on a Thursday between 2:30 pm-6 pm , but only with an appointment, which you can make by calling 02514925108.
There is also a Kita-Navigator for Münster where you can search for a Kita near you.
Here is the link: https://muenster.kita-navigator.org/suche . You will need this document to register: https://www.stadt-muenster.de/fileadmin/user_upload/stadt-muenster/51_jugendamt/kitaplatz-suchanfrage2021.pdf And for single mothers https://www.stadt-muenster.de/fileadmin/user_upload/stadt-muenster/51_jugendamt/pdf/Bestaetigung_alleinerziehende_Personen.pdf
You can either fill it out together with someone with German language skills in advance and bring it with you, or fill it out together on site at the family office.
Another important piece of information is the compulsory vaccination against measles for children in day care centres.
If your child has not yet been vaccinated against measles: two vaccinations are required at intervals of 4 to 5 weeks.
Here is important information about the vaccination in Ukrainian: https://www.kinderaerzte-im-netz.de/media/622dcd5cb49d38288b06ff9e/source/aufkl-mrna-ukrainisch..pdf
You can find a paediatrician for the vaccination at Wolbecker Str. 56, 48155 Münster, Garcia Pedro Andreo Paediatrics and Adolescent Medicine and Dr. Carlos Pacios Prado, MD
Hope this helps!