Certbot?
It can automate provisioning of certificates using DNS-01 challenges, which have wildcard certificates.
https://eff-certbot.readthedocs.io/en/stable/using.html#dns-plugins
Example tutorial: https://www.digitalocean.com/community/tutorials/how-to-create-let-s-encrypt-wildcard-certificates-with-certbot
Once you do that it puts the cert in /etc/letsencrypt/live/ so you can then do whatever you want with it. You would have to handle distribution manually.
If you want to automate stuff across of a bunch of machines at once, I recommend Ansible: https://docs.ansible.com/projects/ansible/latest/index.html