Yes. Or at the least, they are able to begin learning how to use it. Keep in mind that in the TES universe, Magicka is Aetherial energy that pours in through the holes in the sky that are the stars. Anyone has the potential to learn to tap into and use that energy; it isn’t a matter of being or not being able to use it. There’s nothing to say that someone couldn’t start their training at a young age. I’d even imagine schools in the scholarly-oriented Breton societies of High Rock introduce some fundamentals as part of their curriculum. Furthermore, two children can be met in TES V who are beginning their training in magic: Agni in Morthal and Sissel in Rorikstead.
Nobody in Tamriel seems to reproduce. There are bear cubs and young wasps, but no human children. Some hopeful couples have cribs, though.
The new meet the character news post talks about the Battle Spire, and the character in question has been an apprentice since the age of 6.
In Skyrim, the conjurer Falion in Morthal is training a child, Agni, as his apprentice.
She says: "Do you like magic? Falion says I'm good at learning. I like learning about magic." In other conversations, Fallon and she discuss how learning to focus and concentrate is necessary when dealing with magical forces.
Likewise, Sissel from Rorikstead is also learning magic from Jouane. He avoids teaching her fire magic, but suggests she learn a waterbreathing spell. Again, he emphasizes the importance of concentration.
So yes, a child with sufficient concentration and focus can learn magic from a teacher.
Despite the useful information, that Lucilla Caprenia seems like another the bestest evaaar female character. Anyway, other students start education in Battlespire at 12, wich is logical I guess. Thanks for the link!