Ideally, both, but if I had to choose one: game initialization time.
We could then answer questions like "what's the highest number of games I've had 'open' at one time?", since most people include "initialized-but-no-turns-taken" as "open". Of course, most people joining a game that now becomes full take their turn pretty quickly (?).
Ideally, the game creation time (when the creator made it) would be good too, but, of the 3 choices, initialization time is probably the best.