Not necessarily. First generation stars were, theoretically, enormous both due to low metallicity of the collapsed medium and a higher average concentration of said medium. These stars lifespans were extremely short, shorter that blue giants we see today. So novas due to the death of these stars happened fairly early in the lifespan of the universe (talking about few million years after the big bang).
Therefore, life could have developed in a few tens to few hundreds of millions of years after the big bang. That's still true even if we assume that heavier elements are created mainly when neutron stars collide and not by super/hypernovas as we theorized before LIGO/Virgo observatories.
Consequently, we likely are not a "progenitor" civilization in the universe if we only consider planets formation. We might not see anyone out there either because there's a great filter for intelligent life to emerge (so the bottleneck is in our past) or because few/no civilizations get to have an impact on their host stars (the filter is in our future) that would allow us to see them.