Building without permission is completely legal. You just have to comply with the legal regulations.
But if you want to build 6*6 m, then you cannot avoid a building application. I consider the approval to be a mere formality.
I will quote some basics:
"Which documents are required?
For vehicle shelters that require approval, you usually have to submit the following documents. If in doubt, ask the building authority of your municipality or city.
[*]Structural calculations
[*]Building description
[*]Construction drawings from three views
[*]The estimated costs for the construction
[*]A simple site plan with overview map
[*]The carefully and fully completed building application, available at the municipality, the building authority, or on the internet
[*]The construction project must comply with the development plan
Tip: Manufacturers of carports often provide you with some of these documents.
What fees apply?
Within the rules, erection is free of charge. For an approval, you will learn the exact costs from your building authority.
What deadlines must I observe?
In any case, find out before building the carport what is allowed in your municipality. Building without a building permit is prohibited in Lower Saxony and punishable."