I'd say that for a non-scientist, you should treat it as a non-event -- a paper that hasn't happened yet.

The climate is not something for which you need daily, weekly, or even monthly updates. Rather, this paper is just one more on top of a gigantic pile of evidence that that climate change is serious, something that we can and should do something about.

If the paper passes muster, you'll hear about it then, though all it'll do is very slightly increase your confidence in something that is already very well confirmed. Or, the paper may not pass review, in which case it doesn't mean anything at all, and you fall back on the existing mountain of evidence.

If the paper had reached the opposite conclusion, that might merit more investigation by you now, since that would potentially be a significant update to your beliefs. And more importantly, it would certainly be presented as if it were a fait accompli, even before peer review.

Instead, you can simply say, "I don't know what this paper means, but I already have a very well-founded understanding of climate change and its significance."