Is it really not possible to run an earlier version of OS X than what the machine shipped with?
This is usually the case with new Apple hardware. AirPods version 2 require the latest version of all of Apple's OSs to work. From the fine print at the bottom of Apple's official AirPods page


  Requires an iCloud account and macOS 10.14.4, iOS 12.2, or watchOS 5.2.


This is especially true for new Macs, since the the new hardware requires updated drivers to work. Updating these drivers is non-trivial. Consider the case of Touch ID. That is a whole new subsystem that never existed before and updates to that system (i.e. the T2 chip) also require changes to the OS that Apple does not back-port to older versions of the OS.

One way to run an older version of the os is to use a virtual machine on your new iMac. I'm not sure what the state of VMs is currently, but there used to be Parallels and another that could run older versions of macOS in a virtual machine. This is not ideal, but may help.

Apple does have a 14 day return for any reason policy in the US, so you could return it and reconsider your options.

Sorry for the bad news, but this is how Apple keeps pushing things forward.