But he wasn't. At least in the movie version, he and Banner had failed a few times, maybe more we didn't see on screen. Something happened when Tony wasn't there that sparked Ultron to become aware and catch Jarvis off guard. I'd give him credit for getting it 99% of the way there, same with Vision, but he didn't make that final jump, it happened on its own.

And Jarvis wasn't AGI. Seems like it to us, but since Ultron was apparently the big moment of A(G)I in the MCU even with Jarvis being around all that time, he was just a very flexible and even self-aware scripting that would never do something on his own accord, only following Tony's orders. I think even Ultron catches on to that in the brilliant few seconds of waking and realization with his "why do you call him Sir?"