What reason do you have to believe the person won’t vacate on the 1st? If they’ve stated as much, it’s important for the landlord to know. Burlington has some of the most tenant-friendly rental laws in the US, which in this case could work against you. If the landlord has to evict this person, it could take a long time if they are being truly stubborn about it. Try to figure out a plan B and hope for the best. If you have a signed lease, you do have the right to be in the place when the lease starts, even if this other person didn’t leave yet.