I'm part of Generation Z - which is 1997-2010.
I personally, would be very shocked and try to be fully educated and aware on the situation, and updates. I feel as if everyone, regardless of their generation would try to be fully updated. The difference is that Gen Z was born with access to the internet. Because of that, a lot of Gen Zers use this privilege to stay aware.
Would I volunteer? No. I'm underage. And even if I wasn't, I wouldn't. War is very gruesome and disturbing. I think people who choose to put themself on the front lines are brave, but that's not me. Also, my family would not like for me to leave on a practical sewercide(real word is blocked) mission.
I do, however, think that there would be plenty of volunteers. America could even start drafting.
TL;DR I think everyone would be in shock but be glued to the news. I wouldn't volunteer.