time = money , and configuration managers save you time if done right. You would need to do some rough math to calculate how many hours or labor you spend doing tedious stuff, and then put a dollar value on it. Maybe use the median salary of your position as a reference?

If your company uses a method of tracking hours worked for different projects, you could use that as a source of data for "how many hours spent building a machine". Hardware refresh projects are a good example.

Set up Puppet Server on a VM (or download the learning VM if you are lazy). Spin up a "base build" of a server using your current methods, and install/configure an app. Keep track of time spent. Then make a simple puppet manifest that does all the same stuff, rebuild your test machine, and use Puppet to make the same changes.

Show them how much time you saved, and the dollar value of that time. Then make a pretty graph extrapolating those savings across a hypothetical hardware refresh project (use previous projects for reference if you have the data). Stretch the timeline as long as you need, to prove your point.

Then note all of the other stuff it can save time/money on: security compliance, auditing, etc. Can't really put a dollar value on it, but you can point back to that graph to illustrate the snowball effects of cost savings.

I'm in the middle of a "full rollout" of Puppet on our servers, while we are also engaged in an OS migration. Definitely go in baby steps, with small, simple manifests that only puppetize the stuff that is already the same across the environment.