Passenger Pigeons wouldn’t breed unless there were mass of them around. Today, we could likely do something, like fake it or use artificial insemination or something.
Back then, they were pretty ignorant.
The main cause of the extinction wasnt hunting, but was the destruction of the huge swaths of hardwood forests that was the home of the birds.
wiki: The main reasons for the extinction of the passenger pigeon were the massive scale of hunting, the rapid loss of habitat, and the extremely social lifestyle of the bird, which made it highly vulnerable to the former factors. Deforestation was driven by the need to free land for agriculture and expanding towns, but also due to the demand for lumber and fuel. About 728,000 km2 (180 million acres) were cleared for farming between 1850 and 1910. Though there are still large woodland areas in eastern North America, which support a variety of wildlife, it was not enough to support the vast number of passenger pigeons needed to sustain the population. In contrast, very small populations of nearly extinct birds, such as the kakapo (Strigops habroptilus) and the takahe (Porphyrio hochstetteri), have been enough to keep those species extant to the present. The combined effects of intense hunting and deforestation has been referred to as a “Blitzkrieg” against the passenger pigeon, and it has been labeled one of the greatest and most senseless human-induced extinctions in history. As the flocks dwindled in size, the passenger pigeon population decreased below the threshold necessary to propagate the species.
Even if not a single bird was hunted, likely the PP odd lifestyle combined with loss of habitat would have caused its extinction. Mind you , of course the hunting didnt help.