The Edge of Space is an arbitrary number, that has been classified as 100 kilometers high, Blue origins ship New Shepard reached a height of 100.5 km.
This is different from what SpaceX is trying to do, they are going about twice as high, with a rocket that is designed to put satellites into orbit, so its longer and thinner, it travels at about twice the speed. But it is still an impressive feat that Blue origin did today.