How long can a freshly sanded deck wait before sealing without do overs?
How quickly the pores will close depends on ambient humidity, but I'm having trouble even finding a ballpark. I'd never heard of 'water popping' before. Personally, I wouldn't stain anything that's left my chain of custody after having sanded it, without arbitrarily resanding it.

I think they told you to stain it because they saw you sanding. The wait time after which should be as little as possible. You can either build a tent and heat it, or cover everything so that their greasy hands don't make stains. And then you get to resand it anyway in two months.

At least you didn't do the floor. If you're going to open up pores, then you should coat them immediately, as per the specifications of the product.