Normal person meets an alternate (and drunk, and dickish) Zeltretch and tees them off. Cue getting cursed and cast out into the Kaleidoscope. But this is a guy with A rank luck, and it shows that he doesn't get royally, *royally* screwed over.
He gets thrown into other realities, but usually near other young heroes or people just getting started as being heroes, or occasionally in the place of the normal hero for that world (near the protagonists of other series or replacing the protagonist of a series) and he struggles with them, saved by others or his own luck and growing skill, until he randomly goes careening through the Kaleidoscope again until he ends back up at the Holy Grail War, summoned as Archer again.
Each time he leaves the Holy Grail War, he visits the same dimensions in the same order, but adds more to each time. Sort of like a Pendulum that gets more mass at the apex of each swing, he travels further through the multiverse before ending back up at the same places.
The only reason this guy survives early on is his A rank luck. He outright, straight up gets fucking lucky, no two ways about it. He ends up with people that train him or train with him in low-power / low-ridiculousness settings at the beginning, and its only later, as he becomes more competent, that he ends up thrown into more dangerous worlds/settings (aside from F/SN).
This guy also has that 'Prodigy' skill, which I like to think of 'Shonen Hero Power', because it represents his ability to learn at a ridiculous pace (While not as ridiculous as learning a skill that takes decades to master in a manner of days, it's still unfair).
Does that answer your question?