Precursors are not of the physical realm, or they could've existed in the universe that existed before the main Halo universe. So it's certainly possible.
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It is illogical to believe that life can predate matter. It is a huge assumption to say they predate the entire universe
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They are not of our physics or concepts. They are not support to be possible in our reality. They can literally change the universe's consciousness and in extension the laws of physics to suit their needs.
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You do know the precursors created all matter and life right. They even made themselves physical forms. It has nothing to do with real logic it has to do with Halo logic.