Since time is not physical, it could only affected by gravity in cases where the gravity sourse can speed an object up to near the speed of light. Being a singularity, a black hole is the only thing in the universe that would affect time (I don't think neutron stars would be dense enough). Now, according to the big bang theory, the universe began as a singularity. Time would not have existed before the big bang. I personally do not believe the big bang theory because of a contradiction or two that I have have read, but that's beside the point. As for whether time would pass slower at the begining of the big bang theory, no. Once the universe had exploded and started expanding, it would no longer be a singularity and therefore, it would not have enough density to affect time.