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Puss is seen as an infant or young child in the childhood flashbacks
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We see Puss and Humpty's childhood in the orphanage in the Puss in Boots game
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Assuming Puss was born around 1496-7, he would be approximately 13-14 years old at this time.
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We see the holiday Midsummer's Eve, which is June 23, and we see the Tuesday dance sign. The only year Midsummer's Eve was on a Tuesday that fits is 1418.
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Puss, Kitty and Humpty chase Jack and Jill and get the beans.
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Puss returns to San Ricardo and returns the Golden Goose to its mother.
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Assuming the Cat Cantina is only open during the night, after Puss exits, it had became the next day.
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We see at the end of Puss in Boots, Kitty and Puss venture into the same desert that this game starts in.
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The game features the same areas as both other Puss in Boots games, so it's likely not too much time later.