So everything in space, every object had to get to where it is via time. It travelled there. Everything can’t be anywhere without time as without time it wouldn’t have been able to move there. Time is a constant graph, and as it moves forward, things move around and as such, space is able to exist. This is why we consider space and time to be linked.
Now consider this: if one was to plot a graph of space and time on an x y axis to track an object, there is a point on the graph where time has to be zero, and as such space has to be zero.
This is the big bang.
It is the beginning of the graph. When time was zero, and as such so was space.
Space did not burst out from a single point that we could find out there in space, as there was no point. everything was still everywhere much like it is now, except everywhere just so happened to be so close to one another to be at the same point on the graph. When time began, it just about instantly expanded out, everywhere in every direction. There is no ‘center’ to this expansion, just like if you blow up a balloon there is no center on the surface of the balloon, it just expands everywhere, and more importantly with time we are able to quantify this.