Would it be incorrect to say the universe was a single point at one time? That's been my layman's understanding - the universe at the start was infinitesimally small (a point) and has been expanding since.
Would it be incorrect to say the universe was a single point at one time? That's been my layman's understanding - the universe at the start was infinitesimally small (a point) and has been expanding since.
It wouldn't be correct. First of all, we don't know what happened in the first fraction of a picosecond after "time zero", because we have no working physics for that. For the period for which we believe that we have a fairly good understanding, if the universe is infinite in size now, then it was also infinite in size at that first picosecond. It was just inredibly more dense and hot.
Sometimes "universe" is used to mean our observable universe (the part of the universe cut out by our past light cone), which is finite in size. The size of the portion of the whole universe that is our observable universe can be extrapolated back towards the Big Bang, and it would have had a radius of about 10 light years at 1 second after the Big Bang, or a radius of 1 AU (distance of the Earth from the sun) at 1 picosecond after the Big Bang. But again, that's only an arbitrary portion of the whole universe that happens to correspond to what is observable to us (where light had had enough time to reach us). The whole universe, on the other hand, if infinite in size, would still have been infinite in size all the way back to the 10^-43 seconds or so where our physics break down.
As an analogy, if you take the real number line (from minus infinity to plus infinity), and divide all numbers on it by 10 (basically compress it by factor 10), then it would still be an infinite line. No matter how often you repeat that division, and compress the numbers closer and closer together, the line would never become a point, it would always stay an infinite line. Only when you consider a finite segment on the line, for example [1, 2] (the interval from 1 to 2), then that interval would become [0.1, 0.2] by the division, and then [0.01, 0.02], [0.001, 0.002], and so on, and would approach becoming a single point in the limit. But, back to the Big Bang, we don't know what happened at the limit, and the whole universe is more than just the one segment.
One aspect in which the above analogy is misleading is that the universe has no “middle point”, the way the number line has a zero point. The expansion happens equally at every place in the universe. There is no absolute coordinate system relative to which it could happen. It's more like an infinite graph paper you zoom in and out from. The zooming is independent from where you imagine doing the zoom; it zooms as a whole.