Short answer. Yes. A minor can acquire possession of property in his own name; what he cannot do alone is exercise the rights that possession gives him. For that he needs the assistance of his legal representative. The property is the child's — the representative only acts on it.
What the law says
Minors and incapacitated persons may acquire the possession of things; but they need the assistance of their legal representatives in order to exercise the rights which from the possession arise in their favor.
Civil Code, Article 535 — Possession by Minors and Incapacitated Persons. Read the full provision →
Two different questions in one sentence
The article separates acquiring from exercising. Minors and incapacitated persons may acquire the possession of things — that half is flat, with no condition attached. A child can be handed a thing, inherit land, be given a house, and become its possessor at that moment without anyone's approval. The condition sits only on the second half: they need the assistance of their legal representatives in order to exercise the rights which from the possession arise in their favor. Possession attaches to the minor; the machinery for using it runs through an adult.
Why the distinction is not academic
Families routinely put a child's inheritance in an uncle's name, or an elder sibling's, on the belief that a minor cannot hold property at all. The article says otherwise, and the workaround creates the very problem it was meant to avoid: property recorded in the name of someone who is not the owner, an adult with apparent authority to sell it, and a child who must later prove a claim the paperwork contradicts. The lawful route keeps the minor as possessor and lets the legal representative act for him rather than instead of him.
What the representative can and cannot do
The word is assistance. The representative's role is to make the minor's rights usable — to demand the property back, to collect what it earns, to answer for it in a proceeding — not to take it over. Nothing in the article converts the representative into an owner or gives him a free hand to dispose of what the child possesses. Acts of disposition affecting a minor's property are hedged about elsewhere in the law with requirements that exist precisely because the representative's interest and the child's can diverge.
When the minor grows up
Reaching majority does not create a new possession; it removes the need for assistance over one that already existed. That continuity matters when a period of time has to be counted, or when the question is who has possessed the land since a grandparent died. If you are sorting out property involving a child, the documents to keep are the ones showing the child as the person to whom the property came — the deed, the extrajudicial settlement, the receipt — even where an adult signed for him.