Using this ACME client https://gethttpsforfree.com/ one can get a Let's Encrypt signed certificate from an existing CSR. I cannot recommend this solution, but this person is using it How do I to find my Let's Encrypt account ID when using https://gethttpsforfree.com/? And you will need to repeat the process every time you need to renew the certificate.
There are very likely other ACME clients that behave in a similar fashion.
Here is a list ACME Client Implementations - Let's Encrypt