If you don't have a dedicated test environment, your production environment is your test environment. This can be quite frustrating when making big changes. The "scream test" shouldn't be needed for planned changes. One solution is to reuse replaced hardware for testing. Old servers and workstations, too out of date or insecure for production use can be right at home in a testing environment. You hope that everything is the same as production, but some testing is better than no testing. Just make sure these out of date and lower managed devices are sufficiently quarantined.
Another technique is to choose a subset of users of every department as guinea pigs. You will often find users willing to volunteer, as long as you don't push them too hard. In some companies the multi-department approach is necessary because of the drastically different workflow between them.