True: For an officially supported version of a mac operating system you have to go with a maximum of El Capitan.
However, you may insist on installing macOS Sierra 10.12 on this unsupported machine.
That is made possible with overriding the Apple blacklist that prevents installation and results in the "No Entry Sign". This can be simplified with Sierra Patcher.
-Early-2008 or newer [… ] iMac, […]"
Known issue: There might then be issues with WiFi/Airport on iMac 8,2 models if they have an incompatible Airport card installed. Sierra lacks drivers for these. But the cards may be upgraded or an external adapter used.