Then, one day, they hear about it in the news, because there's now some hype, or some event that makes it newsworthy. This makes it feel like the breakthrough was instantaneous or steep, but in fact has been in the making for decades or even more.
I have no doubt AGI is coming, but it will be gradual and slow. It will be the accumulation of more advances in everything, including hardware, as well as software. It might even include economic changes.