if i throw a coin is not obvious that it will be heads or tails
i may believe that will be heads
you may believe that will be tails
other may say, i don´t know what will be.
I think you mix in hope in your definition of belief.
"Either you accept something as true, you are uncertain, or you do not accept it as true, and if you hold one of these positions, you need to bring something new to the table to change the position."
here we try to answer a question with an uncertain response namely if god exist.
you have right we can accept, reject or be uncertain when we try to answer this question
the uncertain or "i don't know" posicion is not a committed posicion.
if you are an atheist-believe, you choose to commit yourself to the "god not exist" position, obviously you cannot prove it.
if you are an theist-believer , you choose to commit yourself to the "god exist" position, obviously this also is unprovable.
the choice is obvious in each case