It is normal for the site to be offline when you do a rebuild.
Solutions are to use a two-container install, which lets you build a new container, so the downtime is less than a minute, or to contrive to have a “we’ll be right back” page display while the site is down, which doesn’t change down time, but then everyone knows that you’re aware that your site is down.
Everyone thinks that at least one of these solutions is too hard and totally not worth the trouble.