[Question] How can there be a godless moral world ?

When searching for ideas and arguments for a post I intend to write on theism, I came upon a comment by Scott Alexander who claimed that many theists would change their mind if you could convince them on a gut-level that there could exist a godless moral world.

I introspected and realized that not only did I not believe on a gut-level that there could be such a world, I also couldn’t think of any convincing argument to imagine it intellectually at least. I also realized that even though it may not be sufficient to convince me of the inexistence of God, it would be a strong blow to my faith nonetheless, and it’s almost definitely a necessary argument to atheism.

I’m pretty sure such an argument exists because there are so many atheists on this forum who seem convinced via reason that the world is godless and moral.

Therefore, I would be grateful if someone could give me not only reasons why and how there can be a morality without God, but also arguments that could speak to my gut-level.

Disclaimer : please do not post arguments against the existence of God. This is not the subject of this question, and I intend to give a better opportunity for that later. I fancy myself a rationalist, but I am also a devout theist, so please don’t make appeals to obviousness or general trustworthiness of a certain category of people (in my experience, it’s pretty obvious that God exists, and devout theists are the most trustworthy people I know—on an intelligence basis).

Edit (to take into consideration the first comments) :
By “a moral world”, I mean that many actions or states are categorized as good or evil, and that this is a good measure to evaluate whether we should do these actions of reach these states, regardless of other measures such as expected utility or pleasure.
For example, I can understand why societies that discourage murder will probably fare better than societies that promote it. I don’t understand why murder is bad, if not because God said so.
(Argumenting that my understanding of morality is flawed is welcome too.)

Edit : This question did not have quite the effect I expected it to have… In fact, it probably reassured me in my faith. For everyone who would have preferred to find more convincing arguments, I refer you to this post.