The original ePrivacy Directive that created the cookie banners is from 2003, and EU users have been seeing cookie banners since then https://en.wikipedia.org/wiki/EPrivacy_Directive#Cookies

The GDPR is what really gave it enforcement teeth though and that's when it really exploded and made the banners more intrusive and adopted by non-EU-native websites that weren't based in but still did business inside the EU.