What you say, is merely based upon the assumption that all matter in the universe, spread outwards at an 'infinitely slow' rate. You have given no logic to back up such a claim of infinite slowness in outward spreading. Obviously you are trying to insinuate that if all matter was focused on one point, that the gravity of that point, would be so strong that a black hole would form, basically stopping all matter from expanding outwards. To this, I say that even thought there may have been the density of matter at that time, in order to create a black hole. In order to understand my explanation for a way around this, we'll need to consider my own theories on black holes and fundamental particles: There were unfortunately no higher forms of matter at the moment of the big bang, and even shortly afterwards, which could be effectively held by a black hole. I am not a believer in the old saying "Nothing can escape a black hole", because I fully believe that it can. Some say that photons cannot escape a black hole, but I think they don't, mostly because when they enter the singularity, they are recycled into more more fundamental particles, before they can escape again.
Therefore, in the beginning, the state change from energy to the most fundamental particle, would be such that a black hole could not hold anything, nor recycle anything because it was already the most recycled form of matter (A fundamental particle).
If matter began as 'atoms', then maybe a black hole would form and your whole 'infinite slowness' would occur, however, they did not begin as atoms, they began as particles which black holes simply cannot hold, nor recycle. Even if a black hole did form, and managed to swallow whatever higher forms of particles had formed, the black hole would merely recycle them down to fundamental particles, whilst the vast majority of matter would still be fundamental, and therefore have the time to escape outwards in all directions, diffusing into 'empty space', which we know, is the quickest kind of diffusion. Basically, by the time matter started to become in the majority, higher forms of matter; it was already too late to stop the matter with a black hole. Matter had already expanded beyond reach, and has continued to do so until the present day.

This is my theory of it, anyway. So yes, a beginning IS possible.