Let’s Encrypt logs all issued certificates to public Certificate Transparency log servers. These certificates can be retrieved by anyone, using the mechanism described in RFC 6962. A number of other CAs participate in Certificate Transparency as well, and Chrome is going to enforce this by November, so by then all newly-issued certificates should be logged.
https://crt.sh/ is one site you can use to search through all certificates known to Certificate Transparency log servers. I think they support RSS if you want to automate a search in some way.