There is no "public" aspect to SharePoint. External users must always be invited.
External sharing is disabled by default on standalone (non-Team connected) SharePoint Online sites (Teams connected sites have external sharing enabled by default). You can request it to be enabled on your new site request form, or to have it enabled on existing sites, site owners or administrators should submit a Help request to https://uoft.me/sharepoint-gethelp. External sharing must be enabled at the site collection level in order to invite external users.
NOTE: Once external sharing is enabled, anyone with the ability to share files (usually Edit level permissions and above) can now share any file(s) with any external user(s). Check your sharing and/or permission settings to determine if this risk is acceptable for your site. Also consult the Guidelines for Protecting Information in SharePoint to determine if external sharing should be enabled based on the data classification.
SharePoint sites have advanced features to protect unlimited sharing. These include limiting the domains files can be shared with (for example, preventing sharing with gmail users) or to forcibly expire guest access. Submit a ticket to learn more.
There are also different requirements and limitations for sharing at different levels (site, document library or list, folder or item) and also based on the external user's type of account.
Please see this additional reference document for details on how to share at each level: External Sharing in SharePoint Online