God probably just made the temple appear along with the traps and the invisible bridge. And every 700 years or so he brings in a new knight to become its guardian.

Agreed. And if the Grail works as it does, who is to say the traps themselves are not magical in some way also?

It's a movie dude. You have to suspend your disbelief in order to enjoy the film. I mean why does the Holy Grail work? Meh it does.

Silly me, of course, the Knights FOUND the Temple, that makes way more sense! Also good point on bringing up the time period of St. Anselm's lifetime, I normally just interpret these dialog infos as some offhand babble to give the story more substance, but that shows the writers knew what they were doing, putting it there exactly to explain the kind of stuff that isn't explicitly shown.

The grail temple must have already been there. For one thing, the grail knights probably didn't simply find the grail buried in the sand somewhere. The grail knight we see in the film probably defeated another grail guardian in single combat, just as this one expected Indy to do.
Another reason, which I am sure George Lucas or Menno Meyjes didn't think of, is that the grail temple would have taken hundreds of skilled labourers decades, perhaps a couple of centuries to build. Three knights? Forget it. And granted, the story of the three brothers says that two of them trekked out of the desert 150 years after having found the grail (only one of them made it), and told the story to a Franciscan friar. Now, while 150 years is still not enough time for three guys to build that temple, there is also the problem with Henry's statement in the scene where he tries to convince Indy to go to Berlin:
H: "He who finds the Grail, must face the final challenge."
I: "What final challenge?"
H: "Three devices of such lethal cunning."
I: "Booby traps?"
H: "Oh, yes. But I found the clues that will safely take us through - in the chronicles of St. Anselm!"
And there's the rub. Anselm of Canterbury died in 1109, long before the two brothers would even have started on their trek home. The only way Anselm could have known about the final challenge is if the temple already existed in his time, and probably had for a very long time before - and some information had trickled to Europe by then.