The heart of it is really. The universe could be one of Trillions and trillions and trillions and trillions of different ways. The VAST majority of those different ways the universe COULD have turned out would mean life would not be possible on eath. But we ARE alive. SO, given that there IS NO GOD, why is it that the universe happens to be so amazingly fine tuned so that we exist?
It's actually saying the opposite of what you said. Not that the Universe just couldn't be any other way but that the universe could but just about ANY other way and most of those other ways don't have life. It's like rolling 10 thousands dice and getting them all to come up ones. Cause all those ones are the only way WE could exist. All the other possibilities would mean a lifeless universe.
The most common solutions to this is that there are multiple universes or the various constants of the universe vary throughout space. We simply happen to live in the one universe that has the right numbers. In other words we are NOT special.