I would add that Moria's extent and population at the end of the First Age were not what they would later become. Others have pointed out that the West Gate wasn't built until SA 750 or later; and Gandalf towards the end of the journey calls the East End "Old Moria." Remember that Moria's population was greatly swelled in the early Second Age by refugees from Nogrod and Belegost.
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The entire plot of The Lord of the Rings could be said to turn on what Sauron didn’t know, and when he didn’t know it.
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