Any finite field extension (in particular Galois extension) of $\mathbb{Q}$ is ramified. Is there an intuitive geometric explanation of this fact?

Suppose we have an number field $K$, is any Galois extension of $K$ ramified? I think the answer is no, but I do not have a clear picture, examples will be appreciated.

My main question is the following:

Can we reconstruct the absolute Galois group $\mathrm{Gal}_{\mathbb{Q}}(\overline{\mathbb{Q}})$ using only unramified Galois extensions?