Goose it's very possible.
School in Bavaria is Pflicht for all children who will be 6 by the 30th September that year - so September born kids start at 5 years 11 months and however many days.
Two of my kids are September born.
One started on her automatic start date (two weeks before her 6th birthday).
My other September born was very shy with adults at 4-5, so I decided not to send him to school. I told kindergarten before he started his preschool year that I had decided he should be zurückgestellt (held back a year). The head of kindergarten said yes, he's a bit shy, why not give him the gift of another year to play and be a child - she said to ask the Kinderarzt for a supporting letter and she'd support my request, and I could assume it would be automatically agreed with parent, doctor and kindergarten in agreement. I went to the doctor and asked for a letter without even taking DS with me and he said oh yes, school's a lot for the only just 6 year olds, why not give him the gift of another year of kindergarten, how lovely :o then he pondered what to write and said that if I didn't mind he'd say it was due to ds's "migration background" (DS was born here and spoke better German than a lot of his bayrisch dialect speaking peers, and his older sibling was doing well at school, but the migration background was nevertheless perfectly acceptable as a reason).
Although DS should have been in the year above (by a matter of two weeks) he is actually only the 6th oldest in his class of 25. 7 of the 25 children stayed back a year.
There is also a Czech boy in the village who moved here at 6 with no German and started kindergarten instead of school.
My DD, who started school in her correct school year at not quite 6, is now in year 7 with children aged 12 to nearly 15 in her class. This is the first year of her entire 7 year school career to date that she hasn't been the youngest child in her class. Now she's the second youngest :o
City parents are known to be pushier and to try to get their kids into school early to save kindergarten fees because they are all such prodigies, but rural families view that as tantamount to child abuse and generally keep kids out of school as long as possible, with the cooperation of GP or Kinderarzt and kindergarten :o