singularities - Was the singularity at Big Bang perfectly uniform and if so, why did the universe lose its uniformity?

Am I right in understanding that current theory states that Big Bang originated from a single point of singularity?

If so, would this mean that this was a uniform point?

If so, as the universe expanded, what factors contributed to transforming its expansion in a non-uniform manner, to the point of what we can now observe? E.g., non uniform densities of matter and non-uniform cosmic microwave background noise, the latter we are told being the imprint of the very early universe.

I'm making assumptions here but I would be interested in understanding how, if it started uniformly, what made the universe become diverse.