Flat Big Bang

It is easy to imagine the Big Bang for a universe with positive curvature (closed universe): imagine a balloon inflating and dots on its surface becoming further apart as space itself expands. Then jump to a 3-sphere.

But I cannot imagine how a Big Bang of a flat or negative-curvature universe could work. In one moment, the universe is zero-dimensional thus finite, the next moment, it is infinite by virtue of its flatness, nevertheless, the universe grows in size. How can the infinite grow?

If the universe is flat, does it have infinite mass?