When you download Godot, it comes with a handful of template samples that are already fully functional games and can immediately run right out of the editor or be made into a test build with no additional configuration required. It's also such a lightweight download (just a couple dozen MB in the auto-installing steam version) that it only takes seconds from when you first web search it, to when you're running it for the first time and so you may as well just download the engine outright for a demo of itself.
Unsure about the other engines but try searching engine names on itch.io, lots of game jam participants mention the engine used in their submissions.