One would have to be considered an adult to receive a land grant, which in 1762 would have come from the British colony of North Carolina.
Two website about NC land grants (neither mentions age) are:
My understanding is that the age of majority in the original colonies was 21 (only reduced to 18 in the 1940s). However I suppose you could give an incorrect age when seeking a land patent although this might risk a challenge to the title.
Dear Mr. Swindale,
Thank you for posting your request on History Hub!
For a detailed discussion of legal age within the British Colonies under British common law, we suggest that you review Chapter 17 of Sir William Blackstone’s, Commentaries on The Laws of England, Book 1.
We hope this is helpful. Best of luck with your research!
Blacklock is, unfortunately, inconclusive
"So that full age in male or female, is twenty one years."
"An infant may also purchase lands, but his purchase is incomplete: for, when he comes to age, he may either agree or disagree to it, as he thinks prudent or proper, without alleging any reason; and so may his heirs after him, if he dies without having completed his agreement."
So the land office might accept payment for entry into a parcel of land but anyone under 21 at the time might disagree with the contract (and ask for his money back? ). Unlikely in practice.
I suspect that anyone judged old enough to farm the land would be granted a land patent.