Infinity and singularity are mathematical constructs. They look great on paper, but we don't know if they have actual physical analogs. It could be that relativity and the physics around black holes, the big bang, etc. are wrong.
THIS. That I've seen, the [astro]physicists are confident that there are no actual physical infinities nor singularities. With the public, they'll use those terms for situations "approaching" infinities and singularities. But in private, they're busy using all sorts of clever mathematics and calculations and arguments to avoid having any infinity or singularity occur, even on paper.