My experience shows
The construction site power box also has a meter number as already said, if you have a meter you can choose the contract ;)
Well, that doesn't necessarily have to work. Providers can block that (was the case here). Therefore, we moved the house connection inside as quickly as possible before the house was heated up.
Because if you put aside heating/drying with electricity, not much electricity is used for construction power. It's a few hundred euros for a single-family house. Whether the kWh costs 10 cents more or less doesn't make much difference.