The first memories I have of using the internet in general are watching Game Theory / Pokemon let's plays on YT, with MunchingOrange's LP of SoulSilver being one of my favorites. As for my first memories using the internet on a computer, the earliest one I can recall is playing Super Mario Flash / Flash 2 after searching for a Mario game (didn't have any for my DS but had heard of the franchise through YT / school), likely around 2013/2014.