You gotta be kidding me. It was an accident because Marle couldn't control her anxiousness. In a way, you can say it's all thanks to Marle the world was saved. However, if she would've slightly felt different and not pressed that button, they'd have never known. If there was something like The Entity involved, I'd imagine he'd force them to learn about Lavos, instead of letting it depend on a small stroke of luck.
Right. Here, lets perform an experiment: hit random buttons on your computer and see what happens. Did you open up a video file? Did you open up ANY file? Yeah, that "small stroke of luck" wasn't so small. Assuming that the computer terminal was at all similar to a modern keyboard that would offer around 114 different single key strokes. Now running a video log wouldn't be that simple, at the very least requiring three (but probably more) keystrokes. Thus, if my calculations are correct, offering 1,481,544 different possible combinations. 4 Keystrokes? 168,896,016 possible combination. Yes, terribly likely that random happenstance is what caused Marle to happen to hit the proper combination of keys that then displayed the Day of Lavos.
So we have "spatio-temporal hyperlinks" (aka, magic doors) that
just happen to connect 6 time periods that were important in the history of the earth and Laovs. On top of that, we have Marle who
just happens to accidentally access a computer file that relates to Lavos and the destruction of the future. And, of course, let us not forget that the people who found these magic doors
just happen to be both willing and capable of taking on Lavos.