Throughout history people have attributed many phenomena to God and then shown them to be caused by natural mechanisms. The attribution to God was a move of faith, whereas natural mechanisms stand as discoveries. An inductive argument could be formed from that to show that it is rational to not believe God is responsible for something. This pattern of God-didn’t-do-it has gone on so long and with such reliability that there are next to no phenomena left to hide God in. And even if you could hide your own God hypothesis in some unknown phenomena, your argument would be arguing from ignorance. We don’t know, therefore…
It is true that I have no idea how the universe got here. But science has collected the evidence, made the evidence readily available, analysed said evidence, make their analysis readily available, and from that they’ve written a lot of the story. There are hypotheses around that initial moment (T0) when things appeared, the most persuasive of which is about the instability to “nothing” and the resultant breakdown into polar opposites. It’s surprisingly reminiscent of Dao Buddhism.
All of the hypotheses don’t matter, though. The question is about how I, and other atheists, can make the leap from I don’t know to not God. The answer is that we don’t have to make that leap. If the answer is “I don’t know” then we sit with “I don’t know”. We do not accept any hypothesis regardless of evidence, especially if the only reason for the hypothesis is that it’s protected by antiquity. To engage with discovering truth and rejecting falsehoods you need to bewilling to not know a lot of things; you need to be willing to not have a one-size-fits-all-unknowns answer to all difficult questions.
The idea that God does not exist is not a humble opinion. The Ignostic Atheist is working on a lowest common denominator of God; he wants to know what the least a being could be and, if discovered, be called God. Without a concrete answer to that question the word “God” is a sound with no meaning attached. So, to move this conversation on, go help the Ignostic Atheist. The concept of God, at its most vague and nebulous, is unsupported by evidence. The hypothesis “God did it” has been falsified for event after event. Evidence for God has been demonstrated to be incomplete or mistaken again and again. These are characteristics of any fictional being you care to mention.
As with all science, there is no certainty. Every experiment gives us more confidence in an existing idea, really confuses things or overturns all existing ideas. No idea based on evidence can ever give us 100% certainty. But, without ever being entirely certain, we have built supercomputers, landed on Mars, been to the bottom of the ocean and run the Simpsons for 25 years. There is merit in the method of never quite knowing.
The alternative method is “faith”. And that’s just unreliable