What if, a blackhole collects enough matter and reaches to a potential singularity similar to t=0 and explodes again and this is the pattern of the cycle? I believe we can observe this.
lyingbuddha has a point here. If we believe that everything happens naturally, and one-time only unnatural occurrences that can't be explained are unlikely to happen, and that everything we've ever observed in the universe has a natural cause, then wondering if a big bang comes from a black hole makes sense, because it would come from a natural source. But how could it possibly happen, if our math says it's impossible? To identify possible answers you would need to discern the dynamics of a black hole interior.
Just because a black hole interior is untestable and forever hidden from view doesn't mean it's structure and dynamics are unknowable. You need to start with the facts and see what you can conclude. Here's some of the relevant facts. We know from our study of supernovas and accretion discs that matter is broken down into fundamental particles before reaching the nucleus of a black hole. We know from our particle accelerator experiments that fundamental particles are unbreakable. We know that there is no space inside a black hole nucleus, which some call a singularity. We know that where there is no space, there can be no motion. We know that fundamental particles' quantum spin is intrinsic, and remains forever. We know that black holes hold enormous, though finite, heat content from the billions of stars they take in.
From these facts we can be certain that fundamental particles are stored individually in a black hole, maintaining their identity and quantum information. In addition, we know that their motion has been halted, which means that the individual particles are stored right next to each other, with no space in between. This results in great instability and outward pressure from the particle degeneracy pressure from the angular momentum of the halted, yet still there, intrinsic quantum spin. Additionally, the enormous heat content is held entirely by the nucleus of individual particles, resulting in astronomically high, though not infinitely high, individual particle temperatures. The thermodynamics of the trillion degree individual particles alone is enough to make you wonder how gravity can possibly hold it in. Yet, gravity does dominate, though barely. We also know from beta decay that the weak force is always trying to push partially outside of matter to work as electromagnetic fields and charged particles, but it's trapped entirely inside the black hole, which has a neutral charge. And we know that the unconfined strong force has been freed from binding duties, since gravity binds the black hole nucleus, freeing the strong force to work towards recapturing the space needed for hadron formation.
These pressures and instabilities grow and grow as mass is added, right up until the day that critical mass is achieved. On that day, just like the day of collapse to neutron star and the day of collapse to black hole, inward forces exactly equal outward forces. Add one gram of matter on that day, and the internal pressures become too great for gravity to hold, leading to uncontained expansion of the nucleus in a big bang explosion into the open spaces of the universe. The natural triggering mechanism is the combination of halted intrinsic quantum spin, thermodynamics of trillion degree individual particles stored right next to each other, the weak force pushing out and unleashing electromagnetism out into the open, the unconfined strong force pushing out to recapture space for hadron formation, essentially, all of the other forces of the universe all working together to overcome gravity, once critical mass at cosmic mass limit #3 is surpassed, on equilibrium day #3.
So is it that hard to believe that a big bang could come from a black hole? Think about it. If you had the desire and ability to launch a big bang of your own, and you went searching the universe for supplies to begin your preparations, the only place you could possibly find your essential starting materials, namely, trillions of solar masses worth of individual trillion degree fundamental particles, is inside a black hole. Further, if you decided to prepare today and launch your big bang tomorrow, the only place you could possibly store your particles overnight would be inside a black hole. For that matter, the only possible way to pull trillions of solar masses worth of fundamental particles all together to a single location is via the mechanics of a black hole. This would seem to indicate that there is no other place that a big bang could possibly originate from other than a black hole.
So do you still think that gravity is so great that it can never be overcome? Even under the present day theories of expansion of space itself, we hypothesize that the space between the early universe fundamental particles expanded, even though we would have expected them all to be captured inside a black hole, because they were so full of heat content and kinetic energy that no attractive force could possibly bind them, not even gravity. So when a black hole reaches the mass of our own big bang, and the individual particles inside are equally as full of heat content and kinetic energy as our own early universe particles, why shouldn't we expect gravity to fail again, just like it already failed at least once before in our own early section of universe?
It should be noted that if c is the universal speed limit, then nothing can exceed c, including an escape velocity. Just like free fall speeds and terminal velocity can never exceed c, escape velocities can never exceed c either, irrespective of what our math might show. When uncontained expansion (explosion) of a black hole nucleus occurs just beyond critical mass, it goes off at precisely the speed of light, meaning that the shock wave goes off at the speed of light, and the particles somewhat slower. Particle interactions and the quick formation of quark-gluon plasma slows the particles down even more, but the shock wave propagates outward in all directions at the speed of light. This is no coincidence; in fact, the big bang shock wave establishes the maximum velocity possible. Nothing can exceed the velocity of the big bang shock wave, and the fastest things, like light, can only match that speed. But since the particles move slower, this assures that no particle or light emanating from any particle can possibly escape beyond the shock wave, because the particles move slower. This means that no outside observer can possibly see the big bang coming until after the shock wave has passed, making us invisible to outsiders. We've had lots of fun over the years saying that nothing can escape a black hole, but the real answer is that nothing can escape a big bang shock wave.
For fans of spacetime curvature theory who might be concerned because the curved spacetime of a black hole means all paths lead toward the singularity, you need to understand that a big bang from a black hole is a cosmic trade, whereby the center of gravity is traded in for an ever-outwardly expanding universe section of matter, permanently freed from the original center of gravity, which instantaneously ceases to exist. This instantaneously flips all the spacetime curvature pathways outward, because spacetime curvature correlates with what the matter is doing.
For fans of the cosmic microwave background (cmb), big bangs from black holes are very similar to the theorized big bang under expansion of space, in that the quick formation of quark-gluon plasma is very near the beginning. So to the extent that our big bang resulted in a cmb, big bangs from black holes result in the same cmb, but with a big difference. The cmb is not spread evenly throughout the entirety of the universe, but instead, is spread evenly throughout the localized area inside of the big bang shock wave only, but it looks to us like it's distributed evenly throughout the universe because we can't see beyond the visible universe.