New stars aren't directly born in the exploded remnants of massive stars. Star formation does not occur in newly produced supernova remnants.
Instead what happens is that, over the course of millions of years, the gas in the supernova remnant is mixed into the gas that is already part of the interestellarinterstellar medium, and which is composed almost entirely of hydrogen and helium. The dilution factor is large, such that after mixing, the gas contains (currently) just 1-2% by mass of elements heavier than helium.
Star formation may then take place if this gas is compressed or otherwise becomes unstable to collapse.
Highly relevant:
How can there be 1,000 stellar ancestors before our Sun?