This lets us know that upon Luigi telling him that he won a mansion in a contest he never even entered, Mario arrived at the mansion and clearly didn't see E. Gadd while doing so. But the question is why did Mario arrive first, why didn't he and Luigi arrive in the mansion together? Well we actually have an answer to that. Upon entering the mansion to start Area 1 we see a Toad who tells Luigi, that Princess Peach asked the Toads to look for Mario after he left when he heard Luigi won a mansion.
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What this means is that by the time Luigi told Mario about the mansion Peach and some other Toads were there when the news broke. If I had to guess what location when they heard the news it's likely at Peach's Castle so for Luigi must've had to call him via phone or send him a letter to Mario in order for Mario to get this news.
Now let's talk about Mario arriving in the mansion. As I said earlier Mario's capture doesn't seem as simple as Mario getting caught the second he opens the door as it likely took him a while. This is backed up by one of the Toads mentioned Mario having 5 items spread all over the mansion, a cap, a shoe, a glove, a latter, and a star.
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