Installing a window unit in a metal window frame with two raised lips
My solution has been to build up the inner windowsill by temporarily affixing a 2x4 on top of it, and use that raised surface to mount the AC. Depending on the window hardware, you may be able to align this so the window can be closed normally when the AC isn't present, avoiding the need to dismount and remount the adaptation.

This could be made more attractive, of course. But an AC in the window usually means aesthetics aren't a primary concern.