Q in Pinyin is not tʃ, it's tɕʰ, a sound similar but not identical to tʃ that's not used in English. tʃ in Pinyin is Ch.
But Pinyin wasn't standardized until the 1950s, so the Chinese government could have settled on different symbols for their Romanization system for Chinese. Using the letter Q for that Chinese sound seems to date all the way back to Italian missionaries in the 17th century, but the government in the 1950s could have chosen a different letter.
Ch in English stems from Latin use of the letters for K sounds since the 2nd century BC, and has been used for tʃ since at least the time of Old French.