Yes, they can make an account if they want to by lying, but that would be against the rules of YouTube's Terms of Service and may result in a permanent ban on YouTube or other temporary account related penalties. YouTube is targeted at users ages 13 and over and is not made for people under the age of 13 due to the content that may appear on YouTube.
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No, they are not meant to as you are meant to be 13 but you could get your parents to manage it for you. That way it would be allowed. You should not really lie your age but lots of people do it and they get away with it.