Feels like I am of an age (29) that is kind of a cut off point to first exposure to computers being special (my exposure being in 1998). Granted for many by then computers at home were not a big deal in the US, but growing up in Ukraine I still vaguely remember my first interactions with a computer when my dad brought it home from the bank where he worked as a programmer -- we did not get personal computers til later. I don't have precise memories, but remember the general feeling of it being this cool piece of tech and being able to use it as being special, and Starcraft being so awesome. Exposure to video game consoles was also a big deal even beyond this age; it was very rare for people in those parts to have them.
Of course, in other parts of the world it is probably still be a special experience some people don't get to have as a normal part of growing up.
I think its really interesting to hear about experiences outside of the US.
One of my very first memories about computers is watching my dad play single player Quake 1 in his home office. I think that was around 2001 when I was 6y old.
I got my own seperate PC several years later, 2006. We didnt't have Internet connection until 2011 so until then I used all of my pocket money to buy blank CD-R and DVD-R towers and filled them with software and media at local library computers. On one summer school break I drove over 1000km between the library and my home.
During that time I managed to mess around with building games and got introduced to Linux and PHP programming.
After 2011 the internet at home was limited to mobile 2G EDGE speeds (~20kb/s) because during that time 3G was not a thing on Estonian countryside where I lived.
Of course, in other parts of the world it is probably still be a special experience some people don't get to have as a normal part of growing up.