Even if you don't watch the news, it's likely that others will and society around you would change rapidly, though. When 9/11 happened, everyone was immediately talking about it.
It depends on how much you socialize. The most probable is, you're at work, doing your stuff, and just check the news when going home (although people sometimes slack compulsively checking their smartphones or their escapist forums). Less probable but possible, you're on some remote hiliday, trekking for the weekend, or something like that.
Point is, I often feel that if some ww3-sized event was to happen in, say, ukaine, I'd know it instantly, feeling the ground rumble under my feet or something. But the reality is, I'd have to open a "news" channel for that - idling online, checking the news, or chatting with a coworker who did. Until then, full unawareness.
I never expect something huge when, say, I check the news in the morning. Because, intuitively, I think that if it was so huge, it would have affected me in real time. Asteroid-crash-like (and even with that, the tremor would be minimal until the various types of devastation waves truly arrived).