I, too, had this same problem with a site that opens to the dreaded message:
“Not Found: Apologies, but the page you requested could not be found.”
I followed Sarah’s advice and updated home page at Settings>Reading> then pick Front page displays: static page, then pick the home page you want.
That solved the log-on problem nicely. My site opened correctly on home page.
But now there’s a new problem:
The site’s home page is “found” when site first opens, but after moving to another page and returning to “home”, it’s now lost. Again.
Any advice would be most appreciated. Site’s URL = https://www.redshoedesign.net