> You would have to prove that such curious people didn't gravitate towards the church instead of other place because _they were already_ financing such research, meaning, that the research wouldn't have happened in another place/group if the church didn't exist.
There were and are plenty of places beyond the reach of the church, and whilst I wouldn't go so far to say research didn't happen at all there, there was far, far less. The more fundamental the research, the less of it happened. There was a distinct tendency for research to be military related outside of the church.
Even so the main problem with research outside of the church wasn't so much whether it happened or not, but only very few cultures managed to keep the knowledge over time, never mind kept teaching the knowledge over time (not a single atheist culture did so successfully, despite many attempts, the Greek philosophers' culture got lucky because it was embraced by the church, and even among the original philosophers most were not atheists). You could say that only Christian/western civilization, and to a much lesser but nonzero extent Islamic culture (although that was mainly preserved in Christian monasteries as well). When science is not preserved, it cannot be built up, which means it never gets to be really advanced.
What makes these religions special is their resiliency (atheism has been shown by history to be seriously lacking in resiliency), combined with the freedom that existed within them. Firstly, science doesn't happen if it's not tolerated. Secondly, a culture that doesn't stay alive cannot build up scientific knowledge over time. Either will prevent significant scientific development. Scientific research doesn't help anyone if it's destroyed every time a harvest fails, which was the more common case, and such an environment means the knowledge doesn't stay alive, and can't be built upon. Christianity did not just not destroy Greek and Roman philosophy and science, but embraced, preserved and taught it, adding on to it over the centuries until eventually it accelerated. Islam, while it never tolerated muslim scientists to any great extent, had the dhimma system, where they let large groups of non-muslims contribute to society through trade, and this left mostly non-muslim groups that practiced science alive, some important ones as slaves to a court somewhere, who managed to get the knowledge back into the west where the church preserved it. But importantly: science in islamic lands died out. The communities teaching science to their kids dwindled to nothing. All traces of it, and certainly the teaching of it, disappeared from all islamic lands.
Keep in mind that Christians certainly destroyed all scientific knowledge in parts of the world on a regular basis (every century or so). What kept Christian science alive is that the church, and in particular monks, would re-divide the knowledge back into the areas where it got destroyed. The most famous example of this work is the painstaking copying of entire libraries by hand, and sending them to other monasteries.
I think given history there's an extremely solid case there would be no modern science without the church, or at the very least, it'd have taken millenia more to get there.
What scientists get taught in school is only a very tiny part of the equation that got us to modern science, and frankly, doesn't appear to be a very important part.