The relevant trigger is "At the beginning of your upkeep, if you control twenty or more artifacts, you win the game." Because this has an intervening if, it must be true to trigger OR resolve. You can't put the trigger on the stack then get 20 artifacts, it won't even go on the stack in that case. Remember "At the beginning of your upkeep" only happens once.
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You will get a more detailed answer if you post in the Rules Q&A forum.