recovery mode trackpad and mouse on screen

Hold the power button till the iMac shuts off.

Plug in the USB keyboard and mouse into the back of the iMac.

Startup the iMac holding the Command (windows) + R keys on the Keyboard.

Open Disk Utility when you get into the macOS Recovery window panel.

Erase and Format the internal hard drive. (GUID Partition Map/mac OS Extended (Journaled)

Quit Disk Utility and Install the offered macOS. (most likely El Capitan and/or better yet High Sierra)

Then plug in your Time Machine backup and migrate from it when prompted during the initial macOS setup.

You're welcome.

Hmm..... the High Sierra Installer used to have the built-in tools to convert the drive to the correct format.

Try re-formatting the drive to APFS and then see if it will allow you to install High Sierra.

see > https://support.apple.com/en-us/HT208496

At this point you will need to use a USB keyboard and mouse to continue Recovery, Installation and Setup.

For example, the inexpensive Logitech MK120 USB Combo works with all of my old and new desktop Mac's.

https://www.logitech.com/en-us/products/combos/mk120-usb-keyboard-mouse.920-002565.html