No, that's not how it works. One option for verifying your control of a domain is to use an HTTP Challenge. That has the ACME Client placing a value on your local server. It then requests the Let's Encrypt ACME Server to look for them with an http:// GET request.
There are various ways the client does this. Sometimes with a file in a location, sometimes by modifying the web server config, or even manual methods (not the preferred way).
There is no HTTP PUT involved. The Client usually runs on your web server