No, as you indicate, each atomic nuclei was formed in "a" supernova (according to current theory) but many x 10 ^many were formed in each of the ten layers of the many x 10^many superstars that were reacting to fuse elements up to iron56. Each layer is deeper, at higher pressure and temperature, and creates heavier elements from fusion in turn. Before the supernova, H -> deuterium, tritium and He layer is at the outside, and Fe at the inside.
Then, each/some/many/most/all of these manyx10^many superstars went supernova at nearly the same time to produce the elements past Fe56 in the "compression zone" of outgoing fused elements: again, the same supernova can create many tens of trillions of element nuclei: but, if the resulting explosion is symmetric, then only the few elements that are headed in the right direction get to our (eventual) planet.
The closer the supernova's are together, the greater their angle of incidence, and the more likely their expelled residue will get to our planet. The faster the first generation of stars condenses, compresses, and goes through its fusion cycle, the closer it will be to us - if the universe is expanding as theorized.
But, I've never seen a justification (calculation/prediction/article) explaining either "why" the first stars are different than today's (billions times more massive ? Why?) or reacted faster than today's stars: going through in tens of years what now takes thousands or millions of years.
The first stars may have existed in an environment so rich in stellar fuel that a temporary abundance in one area would trigger star formation, which would grow so quickly, and go supernova so quickly, that hardly had it blown its gaseous shell away before several other stars were compressed out of its explosion.
Thus one supernova would trigger others in a continuous cycle like a forest fire.
This compression zone you speak of could have started at the surface of the supernova, with some heavier elements fusing as they were expelled outwards. But more likely the real fusing was going on as the pressure increased downward.
But as more and more shells of gas were blown off, those newly fused elements would be blown off with them, creating yet more pressure behind them, for more new elements to be formed, and then blown off in their turn.
A supernova is a process. It may happen quickly in stellar terms, but there is sufficient time for a great quantity of material to be forged, and expelled in all directions.
Speaking of all directions -- the elements did not make a beeline for this location so we could come into existence here. Rather, our here came into existence where the materials collected.
Because the universe was far denser than it is today.
or reacted faster than today's stars: going through in tens of years what now takes thousands or millions of years.
That follows directly from the larger stellar mass.
Suggested Google search term: "Population III"