Newspaper deliveries are that early in the morning for a reason, so that the customers get their papers early too.
Milk deliveries, bread deliveries etc etc are always early morning drops before the day starts for most people.
The shops will have permission to run those types of businesses and as such will be allowed to have deliveries and thus cause noise at these times. There is nothing you can do to stop the shop going about its business.
I suggest you speak to your landlord about the noise problem if it wasnt mentioned before you moved in.