You can set the Google SafeSearch preferences on a specific browser, but you can't set it across an enterprise. Fortunately, sounds like you just need to set the preferences on a specific Mac computer, and that's easy to do and does persist across reboots.

To set SafeSearch in Google, to ensure that your children only see kid-safe content, simply go to the Google home page and click on "Preferences":

Next, scroll down a bit, and you'll see where you can set the SafeSearch preferences for future searches:

Once you make the change you desire, make sure you click on "Save Preferences" so that it's saved on your computer. Now you can quit and restart your browser and even your computer, and SafeSearch will remain set, as you can quickly see in the search results.

Here, I did a quick search for "butterflies" and this is what I see in the top right:

A really important observation is that you need to set this for each and every browser on your Mac and if you have multiple user accounts, it also means that you might have to do that for each user account on your computer too. Make sure it's set for everyone on your system.

Once it's set for all, you can temporarily disable SafeSearch by simply clicking on the "Advanced Search" link adjacent to your search results, then turning off SafeSearch on the subsequent page and redoing the search. It's still set for subsequent searches, as you'd want, but your search can now include unsafe content.