No.
If you're speaking of a newly built aircraft being built under an existing production/type certificate, there is no minimum number of flight hours -- just a production test flight of an hour or so to ensure everything is working properly before the aircraft is released.
If you're speaking of a new design, again, there is no minimum number of flight hours, just a whole book full of flight testing which must be accomplished to demonstrate that the aircraft meets all the applicable FAA certification standards before the type certificate is issued. After that, airworthiness certificates will be issued for each individual aircraft as that aircraft is produced and determined to be in conformity with its type certificate..
The place to find all this is FAR Parts 21 and 23, and the associated FAA Advisory Circulars.