The answer to this question can be found in Chapter One of this excellent follow up to The Giver. Remember that Matt, because he comes from the Fens, is not given a precise age. The narrator only tells us roughly how old he appears to be from Kira's perspective, so we are not given a precise answer. However, we are told very clearly that he is not yet old enough to have been given a two syllable name, which comes with the onset of puberty. Note what we are told:
An older child, a dirty-faced boy of eight or nine years, still young for puberty and the two-syllable name that he would receive, looked over at her from the place where he was clearing underbrush and sorting the twigs into bundles for firestarting.
Therefore Matt is roughly between eight and nine years old when we are first introduced to him in Gathering Blue. I have not read the third novel in this trilogy, so I am not sure how old he is presented as being in that novel.