Infinity is infinite.
A star collapses.
Event horizon enshrouds a singularity?
"[The star] collapses in on itself, packing first its core, and later all the matter close to it, into a point of infinitesimal dimensions and infinite density — a singularity."
What is infinite is infinite. In other words, for black holes to exist at all, the singularity must be the basis for spacetime itself. The form of the existence of spacetime is the possibility of the singularity. You can not "create infinity". Either it exists or it doesn't, and we know that it does as a matter of logic.