Many a student of cosmology reels at the idea of the universe squeezed into a tiny dense point. How could all the matter (and space!) of the known universe be condensed into such a point? There is just too much of it! Our student is not bemused by another feat of condensation: placing all the particles of an object into close proximity and witnessing drastic downsizing. We are told that most of the atom is empty space with electrons and protons set widely apart, so if you eliminate the space the object shrinks dramatically (I remember reading that if you did this to the earth it would be the size of an orange). But this doesn’t help with the kind of cosmic compression envisaged in the big bang theory (or what I prefer to call the hot speck theory): for placing all the elementary particles of the universe next to each other would still produce a very large object (the size of the Sun, say). So how are we to understand the physics of that original tiny dot? How is such a thing possible? How can you cram that much matter into so small a space?
As I understand it (I am no expert), we are to drop the idea of matter altogether and replace it with energy: that is, we are not postulating a cramming together of material particles such as electrons and protons. Such entities did not exist at the time the universe was so compressed; they came into existence only as the original stuff cooled down (like space itself). Instead we are to envisage a point of extremely high energy sans matter. From this concentrated energy matter is thought to have emerged, by the equivalence of matter and energy in physics. Energy converted to matter in the big bang; it isn’t that the matter already existed then in a highly compressed form with all the particles jammed tightly together. And energy is not something that needs to take up space according to its intensity: you can increase the energy of an object without increasing the volume it occupies. A hotter thing is not necessarily a bigger thing. Suppose we think of energy as oscillatory motion: the more rapid the oscillations the greater the energy. Then energy (motion) can increase indefinitely while not taking up more space. Suppose we say that all the energy of the universe can be condensed into a tiny spot: that occasions no conceptual recoil in our keen student, because it just means that we can envisage a very high degree of energy contained in a small area. Energy has no spatial dimensions; it is, as physicists say, just “work done” (or the potential for such work). So there should be no conceptual difficulty in the idea of a speck with the energy levels of the whole universe; we are not being asked to cram particles into a tiny space. The theory is that this concentrated energy can be converted into particulate matter; it isn’t that all the particulate matter of the universe can be crammed into a tiny spot. That conversion may be conceptually troublesome (though a truism of current physics), but the idea of near-infinite levels of energy in a tiny area is not. The universe as it now exists doesn’t contain such high-energy spots (except perhaps in back holes, and hence not observable by us), but theoretically energy can be raised to arbitrarily high levels without violating any basic principles of matter and space. That is, the hot speck could be incredibly hot without ceasing to be tiny.
So we needn’t be fazed by the idea of a tiny speck containing (potentially!) all the matter of the universe in virtue of its extremely high energy level. This is good to know because we don’t want the universe beginning in a paradox. 
 This is my attempt to make sense of what has long troubled me and troubles many people. I don’t believe I have ever read an exposition of big bang theory that puts things quite this way, but it seems to correspond to the underlying idea (I may be wrong, though).