Cake Wallet has a non-KYC buy option but you need a European (SEPA) bank account.
Kraken offers buying Monero with KYC but excludes a bunch of privacy-hostile countries (UK, Germany, Australia, …)
Finally you can always buy some other coin with low transaction cost (Litecoin, Bitcoin Cash, Nano etc.) at any KYC exchange and swap that to Monero and back. Trocador.app shows you where you get the best swap rates. Normally no KYC is needed.