I don’t know what happens. I made many replies but they don’t appear.
as i said i use many other themes and plugins for delivery systems.
now i used your theme to work on a new project.
previous themes support CSS classes for product availability-purchasable.
.product-item:not(.purchasable) or product-loop.unavailable
So there many delivery plugins or plugins with scheduled time availability that works with product availability points there and you can set them with CSS unavailable.
I will try my next post add an example i build in my theme.