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How can our universe have black holes?

Assuming that we were never inside a blackhole at any point in the history of the universe, how can blackholes exist against Gravitational time dilation?

For any point in space time in the known universe that is outside the event horizon of a blackhole a singularity would require infinite time to form, but astronomers claim we do have blackhole like objects in our universe and possibly in the center of every galaxy as well.

If a massive star in our galaxy goes hypernova today then for an observer on earth its core should slow down with compression due increasing gravity and hence increasing time dilation, this behaviour would be asymptotic. As such would this star ever have a singularity?

For us outside observers how did those black hole form and how did ever grow in size if all the matter falling into it will take infinite time to cross the event horizon?

Or are those objects not really actual blackholes and have no event horizons but something frozen in time due to time dilation at the verge of becoming a singularity?