We keep most breads in the refrigerator, but that's only because it's Florida and we have bugs.

The refrigerator makes the starches tighten up, which is what stale is. Warming will loosen them until cool, when the bread goes back to being stale.

I'd wrap it uncut tightly in a cloth and put it where the temperature is steady (in an inside cupboard perhaps), and where there's no air blowing on it. Or freeze it in an airtight wrap, if you have a fast freezer that won't be opened and closed while the bread is freezing (to limit potential immediate freezer burn), though that's likely to affect the crust.

If you don't mind the crust softening, you can also just put it in a zipper bag with the air pressed out and hope for the best.

Refrigeration causes it to stale....non refrigeration allows it to mold.
but your bread will be fine in a paper bag for 24 hours on the counter.

I put all my artisan breads in the freezer, even for overnight storage before serving the next day. I am not familiar with Greek bread in particular, but I put in the freezer, then heat in the oven before serving. On crusty breads, I put them in frozen to reheat and they come out as if freshly baked.

Bread should be frozen, not refrigerated. I freeze bread as soon as it cools down and just leave out what I will eat in the next few hours.