Straight up, the series is two books so far: 'It Ends With Us' then 'It Starts With Us'. The first one's a complete story, but the second is a direct sequel picking up years later with Lily and Atlas. I'd say publication order is the only way that makes sense.
Some folks online talk about reading the sequel first to avoid the heavy themes in the original, but that’s kinda missing the point. The emotional weight of the sequel completely depends on understanding what Lily survived in the first book. Skipping it would make Atlas’s whole character feel less earned, honestly. The second book is deliberately lighter, almost like a palate cleanser, but it needs that contrast to work.
I read them back-to-back when the sequel came out and felt the shift in tone was a bit jarming, but in hindsight, that's probably intentional. You need that closure.