Mankind all over its past epochs did ask the question, how this huge and materially impressive universe could ever have started its existence. The standard dogmatic answer presently given by the majority of modern cosmologists is: By the Big-Bang! - i.e. that initial explosion of the central highly condensed world matter system! But why - it could be asked - should this system have exploded at all? Perhaps this popular BB-hypothesis of a general and global cosmic explosion creating the world is especially suggestive just in these days of wars and weapons all around. Nevertheless to declare such an initial event as the begin of the universe unexpectedly turns out to be extremely hard to explain when based on purely physical grounds. Though it is easy to envisage a granate explosion causing matter to fly apart in all directions from the center of the explosion, but as a total surprise it is extremely hard to explain which physically operating forces or pressures might be responsible to drive the initially highly compacted cosmic matter agglomeration apart of each other. If the explosion forces are imagined as due to acting thermal pressure forces of normal massive matter, then the needed pressures cannot be due to the extremely high temperatures of the condensed matter, because the thermal energy of relativistically hot matter, as relativity theory tells us, will act as an additional source of gravity, i.e. making matter even "heavier"! Hence this just impedes the initial mass agglomeration to explode and fly apart. As we shall show in the following article the explosive BB- event can only physically be explained, if the necessary pressure is not conventionally realized by the temperature of the gravitating matter, but to the contrary by the immaterial cosmic vacuum. In fact - as we shall demonstrate here - without a cosmic vacuum pressure, the so-called Big-Bang never at all could have happened. Certainly vacuum pressure up to the present days of cosmology still is a fully speculative subject, but it will become evident in the following article, that without this highly speculative, physically handable quantity a primordial Big-Bang would not have happened at all.