I have a question regarding cosmology and the Big Bang. I try to be a strong advocate of science and critical thinking. When we observe the expansion of the spacetime metric, the typical line of reasoning is that in the past the universe must have been compressed to a singularity. However, if I have a latex sheet and I chose to stretch the latex radially outward, while also adding to the sum total of latex. Those living on the sheet would observe the expansion and perhaps through the same line of reasoning conclude that in the past the latex sheet must have been infinitesimally small. In reality it was just a sheet that I chose to stretch out. (Forgive my poor metaphor.) I understand that our universe is very different from this and that is where the analogy breaks down. I suppose that my question is how do we know that the universe was once compressed to a singularity, rather than some finite critical state that resulted in the expansion? There appear to be some discrepancies when determining the age of the universe.