A boy(3 years) I saw in a fun-fair was trying to play in mickey mouse bounce house(precisely speaking clambering a steep slope) suitable for kids older than him, say more than 5 years. I am trying to find a phrase which would mean that he did something which the older kids do because he was determined. I have heard of a phrase head and shoulders above his peers but that emphasizes that he is superior to his peers but I want a term which focuses on the equality between him and his seniors. Looking at him, we feel proud that as a young kid, he is doing really great and is equal to big kids playing with him.
You could say he was holding his own among the big kids.
Hold your own (idiom):
(1) to maintain your position or condition despite difficulties
(2) to be as successful as other people or things in a situation
Hold one's own
(1) be sufficiently competent in a certain situation; "He can hold his own in graduate school"
(2) maintain one's position and be in control of a situation