"The sky is big."
Interesting, I think this question was designed to trick you if you already know Chinese :p In Chinese, 天 is the word used for sky (or more properly 天空), whereas 空 by itself just means space. (This is where you get words like 天気, which literally means something like the temperament of the sky.)
Languages are interesting!
空 is also often associated with the sky in Chinese. Like 空中 means in the sky or mid-air, 晴空for sunny sky or 空投 for airdrop and so on. So for a Chinese 空 for the sky is also quite natural. (I think people used to think there was nothing in the sky, that's why they named it the nothingness above a human's head)
While 大き does have a な-form, just as with regular na-adjectives it is only used when the adjective is modifying a noun. So, it might be used in a sentence like "I think the big sky is beautiful", but not to say that something is big (which is called a predicative use of the adjective). A corresponding example with an ordinary na-adjective might be that "The sky is calm" is 空は静かです。without な, but "He is watching the calm sky" is 彼は静かな空を見ています。with な.