The last time someone became a god in my campaign, all of Absalom lit up blindingly for a bit and then a city-sized face descended out of the clouds, only to be held back by the new deity.
It would've been much harder for anyone in the city to not notice a new god. XD
Yeah I think this is probably how it'd be handled. This is also how Razmir got to be a "God". If you incinerate an entire city people will believe you divine. I'm sure a giant sky-head would have a similar effect, but there's no "proof" for anyone unless you provide that proof.
Lamashtu went from being a demon lord to being a god by killing and stealing a domain from a true god.I think in some of the creation myths they killed some gods. Asmodeus killing his brother, for example. But there is more than one creation myth and Paizo has never said which one(/ones) is(/are) true - if any.
While that is certainly true, I think the matter of Lamashtu's ascension might be relatively well documented.
Most likely, she was already a well known and documented demon lord (at least within the planes). Being the first to transition to true godhood would certainly be an area of intensive research, both by demon worshipers and people worrying about the rise of more demon gods. Given the fact that angels can just be called forth with various types of summoning spells... I think some of the broad strokes should be reliably obtained.
At the very least, it provides an plausible explanation for why Lamashtu is the only one that managed to rise to godhood. Other demon lords would likely find the stunt hard to copy due to the fact that their intent would be rather transparent both to the victim and rival demon lords that would want to interfere.