You don't need to invent all that stuff before your DEM is written.

Don't just say 'Oh, did I not mention I was fluent in Ancient and studied all these control rooms for the last 20 years before you met me?' If there's magic in your world, give somebody a lucky talisman that makes even their trip-and-falls work for them, and show it working on a small scale long before the Big Moment. Build up the parts of that character that make it believable they would be in a position to save everything just like that. Or learning the ancient language - and when they get to the room have them grin and say all that study time was worth it. Have someone sit up late at night reading old notebooks and manuals. If you get to the end and decide you want someone to push a Big Red Button and fix it, fine, but then go back and put the clues in. A certain amount of unreliable narrator, where a character 'steps out to chat with some locals' and then at the climax of the story the locals come riding over the hill with 50 of their friends and save our hero, as we're told that the chat was to plan this exact rescue - it can work, especially if you've shown this character forming strong relationships and understanding the relevant group dynamics of the village or whatever.A series of actions, all in line with the character's, well, character, and all logical things for a person to do in that situation, leading to a success against strong odds - ok, even if the reader couldn't predict some of those actions.A single action by one person (say, tripping and falling and hitting a lever that wasn't marked and that the person had no way of knowing about) completely eliminates all the problems (the multiple antagonists all fall into the open trapdoor, or all weapons stop working, etc) - too much.The same plot resolution in another story might be considered 'too much' to believe.

If everything else is going well, people won't notice that your coincidence is far fetched. He's trying to play (or was it compose?) 'Mary had a little lamb' but was failing and starts banging his head against the keyboard. If anyone's seen Sesame Street, there used to be a skit about Kermit interviewing Don Music. Reading back on 7, the first answer states that what the OP wrote wasn't DEM but a coincidence. Would the MC be able to find their way out of the woods? Perhaps. Is this a coincidence? DEM or Plot convenience? (Or all of the above)? The result of this event is the MC finding the way out of the woods. The hermit gives directions to the MC to get out of the woods. If a MC is lost in the woods and happen on a hermit living in a hut. I feel my understanding is mixed up but aren't DEM and plot-conveniences just (albeit specific) instances of coincidences. Suspect it's the connotations behind those words. I was blissfully ignorant about coincidence, DEM and plot-convenience but now,

One last favor deus ex