Can I install a one-time purchase of Office 2019 on an Azure VM?
There are some complications with licensing in a cloud environment and for many traditional Microsoft products, activation is tied to specific hardware (like a motherboard). With a VM, your hardware configuration changes frequently (every time you deallocate your VM) and you would very quickly exhaust all of your product activations.
Additionally, software installations usually have specific licensing rules because of the increased level of public/user access. For this reason you would want to make sure that use in a cloud environment is explicitly called out in the product license.
For these reasons, you would not want to install a one-time purchase of Office on a VM.
Office 365 - Created for cloud
To address these issues, Office 365 has been designed specifically for the cloud. I know that you said that this isn't an option for your scenario but it would be the recommendation for anyone else who may find themselves in this situation.