if we assume that singulary existed then how long singularity have existed before the big bang
The question 'how long' reffers to the time. For us, space and time appeared at the moment of Big Bang. Most cosmologists insist that time before the Big Bag simply made no sense -- that to contemplate a time before the big bang is like asking for directions to a place north of the North Pole. Before the Big Bang there (probably) was nothing except the singularity. In our understanding, empty space is vacuum filled with non-zero energy (quantum fluctuations). There was no such a state of matter outside the singularity, so 'space' indeed doesn't make any sense before the Big Bang.
The answer to the question may be anything -- forever, 5 human years, 5 lives of the Universe. We cannot know it in principle because our knowledge is bounded by this particular Universe with its space and time. It is impossible to measure or define something that exists outside our universe in both spacial and time dimensions, like primal singularity.
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