Frontend controller to display all products with with layered navigation. Plus widget which pulls through random product(s) from whole of catalog. Any additional rules that would apply to a product collection on your store such as visibility or stock.
composer require dominicwatts/randomproduct
php bin/magento setup:upgrade
php bin/magento setup:di:compile
Go to /all-products or use header link
There is a widget for use in layout, blocks and CMS pages which is configurable via backend.