Why does God allow children to suffer?

There is no answer to this that makes it feel acceptable, and any answer that tries to make it feel acceptable should be distrusted.

Most explanations for suffering lean on human freedom: people cause harm because they're free to choose badly. That explanation runs out quickly here—a child's illness isn't the result of the child's choices, and a famine doesn't ask a five-year-old's permission.

This is a sharper version of the general problem of evil—suffering that falls on people who did nothing to bring it on themselves.

Christianity doesn't pretend to close that gap with a tidy explanation. What it offers instead is that creation itself is described as broken, not functioning as it was meant to—and that this isn't its final state.

It also offers Jesus, who didn't treat children as unimportant, and a promised end to exactly this kind of suffering.

That's not a solution. It's a reason not to face this alone.