The electron is a point particle. To say it is zero would be misleading. The instruments we use are not sensitive enough to measure the true size or location of an electron. Trying to measure the size of a single electron with our current technology is like trying to pick-up a virus with a...
If we could find the point in space where the singularity happened would you expect to find abnormalities in space time? Is there a ground zero, where there is no relative motion where everything is rushing away?