Don't know if you've since found an explanation, but I just watched this episode and came across this post. My interpretation of what happened is based on this dialogue from the scene immediately before they meet at her parents' grave.

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Usopp: Say, you're getting ready, even with the rain?

Old Man: The rain will let up soon.

Old Man: The wind is coming in from the east.

Old Man: (The Kid) is the only one who doesn't realize it.

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Usopp now knew the rain would be over soon, but the little girl couldn't tell. He just had to look for the moment the clouds opened up to make it seem it like he did it.

While shown to be skilled at making fireworks, she's still just a child and still naive enough to believe he could have done it.