The only place "infinite density" could exist, would be at the singularity, which, for a non-rotating black hole is a mathematical point at its center.

I anticipated this answer and I was going to reply:

why would it be a singularity (i.e. of infinitesimal size/smallest possible size) if mathematically, to get the same density you could just take the volume of all the atoms that make up the ''singularity'' and arrange them in a sphere. I don't mean in a way that a normal object is made, constructed by atoms side by side; I mean to make one consistent object/sphere whose volume would be exactly equal to the volume of all the atoms it contains. Surely, following the same logic, this would result in infinite density, or maximum density if you will. Wouldn't this result in a black hole as well, rather than having to somehow shrink beyond that into a singularity?

However, this assumes that atoms are incompressible. If they were, this would be undeniably true. So by infinite density, I meant that it's the smallest possible shape containing normal density and volume of all the atoms, but in the meantime I found out that atoms are in fact compressible and do not have a ''volume'' as I thought they did. Is this true? This goes beyond my knowledge so I can't comment on that.

By the way, if such a thing as Planck length exists, doesn't that contradict the notion of singularity since it would be smaller than that?

It's very hard to believe its existence as its value would, in theory, be ''the first number after zero'', which is mathematically inexplicable.