You seem to be thinking of the Big Bang as an event that happened in a preexisting landscape of space and time. That isn't the way it's described in general relativity, which is currently the only theory of gravity we have that is supported by empirical evidence. Here are a couple of FAQ entries about that:
http://www.astro.ucla.edu/~wright/cosmology_faq.html#BBB
https://www.physicsforums.com/showthread.php?t=506991
But anyway, I think we can modify your question just slightly and come up with an answer that is basically "yes" to an even stronger statement. As far as we know, practical issues make it impossible for us to gain information about certain times and places that existed at t>0 (where t=0, which would be the big bang, doesn't actually exist as a moment in time). For example, the universe was so hot and dense at t=1 minute that the only information we have -- and the only information we are ever likely to be able to get -- about events before t=1 min consists of nothing but statistical averages concerning things like the abundance of certain elements, but nothing whatsoever about specific events that occurred at specific times and places. Any detailed information about events before that has been obliterated more thoroughly than anything written on a piece of paper and thrown into a furnace. So it's not just that we can't access information about t<0 because "the Big Bang destroyed any evidence of any element of creation." We can't even access certain information about t<1 min because the heat of the early universe destroyed any evidence of anything that happened in the earlier universe.
There may also be limits on our knowledge of the universe that are not just practical but fundamental. The universe may be either finite or infinite:
https://www.physicsforums.com/showthread.php?t=506986 We also know that it has a cosmological constant. If it's infinite, then the accelerating expansion caused by the cosmological constant will eventually cut off any given observer from more and more of the rest of the universe (due to a cosmological event horizon), and there will be events in the early universe from which that observer can never, even in theory, receive information, because not even a ray of light could have gotten to him/her from that event, even given infinite time to travel.
Although GR is the only theory of gravity we have that is well established empirically, there are other theories that would allow time to be extrapolated back before the big bang, and there are even theories such as Penrose's Conformal Cyclic Cosmology in which it is possible to get information about certain very specific events that occurred at specific times and places before the big bang.