The tradition view
Amavasya is on many avoid lists for new-home entry. Families who follow muhurat strictly usually skip it for griha pravesh.
The practical view
Movers can still transport goods if the society permits it. The question is whether your family treats goods movement as entry. That answer is cultural, not logistical.
The middle path
Move goods to the new flat, keep puja items out, and perform the first formal entry later. Write any waiting or split-delivery charge before booking.