Typhoon is a word with at least three parents, and nobody is sure how much each one contributed.
The first parent is Greek. Typhon was a giant of Greek myth, and typhon also meant a whirlwind. English borrowed it in the 1550s as Tiphon, meaning a violent storm. Even the Greek word's own origin is unclear. Beekes links it to typhein, "to smoke." Watkins links it to a root meaning "deep, hollow," as in a monster from the depths.
The second parent is Arabic, Persian and Hindi. Tufan means a big cyclonic storm, and in India toofan still means a big storm. Etymonline says the English word apparently comes from it. The Quran uses al-tufan for a flood or storm, including the flood of Noah.
The cyclone sense first appears in Europe in Portuguese in the mid-16th century. The Hobson-Jobson dictionary (Yule, 1903) argues that Vasco da Gama and his crew likely picked up tufao from Arab pilots. That is an inference, not a documented fact.
The third possible parent is Chinese. Cantonese tai fung, "a great wind," may have influenced the form or meaning in English. Merriam-Webster goes further. It calls typhoon an alteration of the earlier form touffon, shaped by Chinese (Guangdong) daaih-fùng, "big wind," and it also lists Arabic ṭūfān and Greek typhōn.
English first used typhoon for a cyclone in 1588, in Thomas Hickock's translation of an Italian account by the Venetian merchant Caesar Frederick. He said that every 10 or 12 years the East Indies saw extremely severe tempests, and that no one could predict which year.
Some sources say the Arabic word comes from Greek typhon. Others consider it purely Semitic, in which case Greek may still have shaped the English spelling. Merriam-Webster's earliest date for the modern sense is 1771, for a hurricane in the Philippines or the China Seas.
So the claim that typhoon simply means "big wind" in Chinese is only part of the story.