The tradition view
For many households, Sawan is devotional and not preferred for new-home entry. Some priests may allow specific cases, others may ask you to wait. Family custom matters here.
The logistics view
Sawan lands in the rainy season. That can mean softer quotes, but also wet cartons, basement loading issues and slower routes. A closed body truck is not optional for a full-home move.
The middle path
If the lease forces movement, shift goods with proper rain packing and do formal griha pravesh later. Keep that split written in the mover plan.