Is it possible to ask the moving company to keep my stuff for 1 week?

I need to move from Tokyo to Osaka for new job.

I finally found a really good apartment.

The main take away is that the current expected move in date is at the end of May or at worst, in first week of June. They cannot give me the exact date yet as the lessee is still in the room. They will only know after GW.

Now, as much as possible I do not want my new employer to extend my start date (5/18) just because of this. So, I am preparing myself to stay in a hotel. But the problem is I am planning to schedule the truck pickup on 5/15. So i will need a service where they can let me store my stuff.

Does anybody have any recommendations for moving companies that offer this service cheap?