No prep, morals off/bloodlusted, random encounter on earth; however, can be taken into space. No BFR, Fight is to the death, Thanos, Doomsday, and Darkseid cannot talk their way out of the fight/trick Amazo. Thanos has cosmic cube, doomsday is H/P, or whichever of his versions is strongest, Darkseid is also at the height of his power. Amazo is the Amazo from JLU where he soloed the JL.
You must have something against Amazo, unless this is the amazo from JLU. looks at OP ok it is. Amazo could destroy Doomsday turn him into bones like imperiex did. Darkseid is getting hurt too. Comes down to Thanos and the Cube, not sure how the cube works because Amazo couldn't hurt solomon grundy's black magic. I know the Cube is not black magic but will have to do more research and get back.
Cosmic Cube makes Thanos a Reality Warper, so he erases amazo from existence. Stomp.
Amazo is also a reality warper, is he not? He made Oa(sp) go to a different dimension because it was in his way, then he brought it back when the surviving GLs asked him to. Maybe that isn't reality warping; I might have it wrong. However, even if I do, what is stopping him from copying the Cosmic Cubes power? Here is the version of Amazo that I am talking about
Also, there are multiple reality warpers in JLU, including Dr. Fate, who couldn't do anything to stop him. Just being a reality warper wouldn't stop him.
Doom with a cube steals galactus power for example:
And again, what is stopping Amazo from copying the cubes power?
Given that the cube was created it means that it is possible to create another therefore it would be possible for comic book Amazo to copy it's power not just the ultra powered animated one. The only thing I'm certain he couldn't copy would be Darkseid's given the unique nature of his power, possibly unable to copy Thano's himself but I don't know the nature of his power.
The team would keep Doomsday at home and Thano's would only use the cube from inside a lead box and they should be able to take this easily given the power Darkseid has had at his strongest.