The short answer is that Lets Encrypt and other Certificate authorities distribute server certificates / private key pairs that are signed by a Certificate Auth

The short answer is that Lets Encrypt and other Certificate authorities distribute server certificates / private key pairs that are signed by a Certificate Authority who has a certificate in your web browser / operating system that can be used to verify that signature. Google “chain of trust”. You can effectively do what you suggested by generating a self-signed certificate for your web server, but visitors either won’t be able to access your site or will need to accept the risk of connecting depending on the browser they use.