You're thinking about it in terms of a fixed amount of stuff, which doesn't quite work, for the reasons you're thinking of. In particular, for any given amount of mass there's a corresponding Schwartzchild Radius, and if you compress the mass densely enough to fit within that radius, it's a black hole, and if it's larger so it doesn't fit within that radius, then it's not.

Instead, though, consider taking a sphere of constant density. If you expand the radius of that sphere, then it's got more stuff in it -- the mass of the sphere increases as the radius cubed.

Now, the trick is because of the interesting fact that the Schwartzchild Radius is proportional to the mass of an object.

So, if you take this sphere, and expand it by adding mass, keeping the density constant, then the gravity slope at the edge keeps getting larger, and eventually it will become a black hole -- no matter how non-dense it is.

An intuitive way to think about it is to imagine that you take a sphere, and pick a point on the surface of it. Now, keep that point fixed, and add stuff on the other side of the sphere to make it a larger sphere. All that stuff you're adding is on one side of that point, so it increases the gravity gradient there. Keep adding stuff, and the gradient gets higher and higher, and eventually it will reach the "too steep" state.