Some days, I even impress myself.
We have a few chromebooks from CDW-G that do not have Serial Numbers printed on them. A web search brings you to developer mode, but you can not do that on a managed device, which these are.
Have your Google Admin Console open to manage devices and you will see a them listed by the day they last synced but before that you will see enrollment day. That's what you're looking for.
Follow the steps to get to developer mode anyway [Press Escape and Refresh and tap the power button at the same time], you will get an error and the device will restart
Now you have to re-enroll it (which just takes signing in with your email and password). While doing this, look at the Console and the enrollment day. One should be enrolled today, the current day, because you just enrolled that device and there is your serial #.