I can't say I thought something was impossible but I have experienced amazement at some games that combined elements from other games in ways nobody thought of yet or just didn't do it well to get noticed for it.
Keep in mind, I was born in the early 90s so I grew up and my first games were physics puzzle games like Crazy Machines on PC, I played the odd Super Mario on the GB and GBC and when Half-Life 2 came out that was exciting to me. First-Person games were new to me then, it was all very confusing at first but I have grown fond of it. So now we skip a few years again, it's 2010 and I got Portal for the 360. I slip into the role of Chell and you are in a room with no door, after a few seconds you hear someone talking to you through speakers, telling you that tests are starting soon. The robot voice is cool and neutral, but sometimes there's glitches and you suspect that something is wrong. Regardless, you follow its instructions. This changes as you progress through the game. She makes you sacrifice someone to get through the next door. You are beginning to think that you should escape and you do in fact find some areas that seem beyond the area the robot designed for you. It's thrilling. You dodge her turrets or deactivate them. You use the Portal gun now not as a testing tool but as a way for your character to survive whatever might want to kill you and to maneuver through areas which can be very tricky at times, thankfully to the training you are prepared for that. At last you face your tormentor and you take her apart, again using the Portal Gun she made you test.
I brought up all those other games because Portal feels like a a good blend of them. You get to do platforming, you have physics puzzles, you view the game's world (the testing areas and later the labs) through Chell's eyes. On their own those elements already made for good games but mixing them together like that? It's like chocolate with nuts for the first time. It's amazing.