When looking at the Euclidean Topology with the base
$\big\{\langle x,y \rangle | \langle x,y \rangle \in \mathbb{R}^2,\quad\exists\;a,b,c,d \in \mathbb{R}^2 such \; that \; a<x<b \quad c<y<d\big\}$
is it possible to have a disk or circle or can one only approximate a disk?
Certainly. But let's be precise. I'm sure you mean a disk and not a circle because the two are very different subspaces of $\Bbb{R}^2$.
One of the axioms of a topology is that an arbitrary union of open sets is still an open set. Thus, you can take an arbitrary union of arbitrarily small (infinitesimal) rectangles in such a way that you get an open disk. This is similar to how we allow the width of rectangles to approach $0$ so that we can approximate the area under a curve by integration.
I suggest you read this post if still confused: Does it make geometric sense to say that open rectangles and open balls generate the same open sets?