There's no consensus in the group of atheists except that they reject the idea of a god. Trying to frame it like there are more common assumptions ("Atheist interpretation: <your assumptions what you and other atheists think>") seems generalizing to me.
Speak for yourself. I'm an atheist and I see how people have purpose and I also find meaning in life (although I struggle with it all the time like many other people including theists).
I think this is pretty universal POV among atheists, but if you disagree - whatever. I never even claimed it's the only possible interpretation.
Avoiding pain and seeking pleasure seems to be a built in goal to almost all living beings.
No living thing creates that goal for themselves, it comes built in.
One of the easiest way to find meaning then, is to strive to reduce other sentient beings sufferings, and to increase their happiness.
There is no need for a god, or an idea of a god to promote this point of view.
This is basically https://en.wikipedia.org/wiki/Utilitarianism and the simple counterexample to that is https://en.wikipedia.org/wiki/Utility_monster
At any rate - it's clear to me that these goals are self-created, and different between different people, so claiming them to be universal seems wrong.
They come with that built into their neurochemistry, and so do we.
It's the closest thing to a universal moral system I could think of.
And I don't see it as utilitarianism, I was thinking of Buddhist ethics which also contains other precepts to counteract some of the pathological cases in utilitarianism.[1]
[1] Does it do so perfectly? Probably not, but it attempts to be a practical set of precepts, you still have to use your brain.
The only goal that all livings things share is the drive to reproduce. Anything without that drive dies out, which explains why it's essential to life.