You definitely can configure Jenkins in a repeatable manor. See https://wiki.jenkins.io/display/JENKINS/Groovy+Hook+Script

You can write all the configuration in groovy and it will execute when the Jenkins process starts up.

There is also "Jenkins Configuration as Code" plugin which allows you to have a single yaml file to configure most of the Jenkins system.

https://github.com/jenkinsci/configuration-as-code-plugin/bl...