I'd like to discuss a major problem I see with black holes (no I'm not the theology anon), here's my problem with the theory

My understanding
>A collapsing star will not form a singularity until r=0

The problem
>As r->0 G->infinity
>Assume this process takes X time from its own reference frame
>We know that time dilation occurs due to gravitational pull based on GR such that ?t ->0 as G->infinity
>Intuitively this means that the collapsing of a star into a singularity would take an infinite amount of time from a reference frame outside of the local singularity

This implies one of two things, either GR fails in a case in which it should apply in which case GR should be reworked/tossed out
Or black holes cannot form within the currently understood age of the universe which either invalidates the black holes hypothesis or introduces one of two things; a much larger timeframe for our current universe if we assume the big bang happened as described by the literature or the big bang never happened at all.

I'm not an expert in the field so feel free to let me know if I've missed some fundamental concept, otherwise discuss.