No, it is not possible, for the following reasons:
1. The Big Bang was and is an expansion of the universe that extends across all space. You can think of the expanding universe and the matter inside of it as being sort of like the raisins inside of a loaf of bread or balls of cotton on the surface of a balloon: as the bread expands during baking or as the balloon is blown up, the particles inside of it get farther apart. It is space itself that is expanding; matter isn't simply moving outward from a single origin point. Black holes, by contrast, are spatially localized: the singularity is located within a specific point in space, and there is space outside of the black hole. There is no space outside of the universe. The universe has no edge.
2. Recent observations of the universe's expansion indicate that the universe is expanding at an increasing rate, as though there is some sort of large-scale antigravity-like phenomenon in effect. If the universe were going to collapse in on itself, then the rate of expansion of the universe would be slowing down, not speeding up. Exactly why this is happening or how it is even possible is one of if not the largest unanswered question in physics right now.
By the way, the hypothesis that you are describing has been thought of before: it is the "big crunch" hypothesis, that the entire universe would one day collapse in on itself. It would not be a supermassive black hole, though, even if it did collapse, because all of space would collapse to nothing, with no void vacated by the collapse. It would be just infinitely dense matter in all "directions", if you could even define a direction, since space would cease to exist. Time would cease to exist as well.
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