Since Gift of Doom and all morph cards do not use stack, is there a way to stop it from attaching to a creature? The wording doesn't sound like a trigger either.
No, indeed, you can't respond to the turning face-up, which is a special action that doesn't use the stack, nor to the attach, which is a replacement effect that modifies that special action by adding something to it. There is no window where you get priority between you knowing this is Gift of Doom and that's it's going on this given creature, and it being attached. By the time you get priority, the creature is indestructible.
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I'm a former judge (lapsed), who keeps up to date on rules and policy. Keep in mind that judges' answers aren't necessarily more valid than those of people who aren't judges; what matters is we can quote the rules to back up our answers. When in doubt, ask for such quotes.
Essentially no. Turning a face down creature face up is a special action which does not use the stack and because attaching Gift of Doom is a replacement effect it will be attached to a creature before anyone can do anything.
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