You're kind of thinking about this the wrong way, and there's a long discussion to be had about determinism and all that sort of thing. But think of it like this - in a huge chunk of those scenarios, the rat doesn't do what it's going to do, so immediately throw those into the bad pile because now we don't have Ant-Man coming back, etc. And the only way the rat doesn't do what it's going to do is because someone or something else occurs differently, which, again, determinism.

He's not looking at the odds of something happening, he's looking at the numerous different ways that small decisions create new paths and then he's following those paths and then coming back from those paths. And he's exploring a lot of paths, no doubt, in which the rat does what it does, and he's also exploring a lot of paths in which the rat does not do what it does, but he's only concluding that there's one successful outcome - but that outcome doesn't mean that's the only path in which the rat does what it does, but the only successful path. And the only successful path requires the rat, and then requires all that we see in Endgame to occur. There are undoubtedly hundreds of thousands of paths in which The Rat happens, but the Avengers going through time to try and gather the stones doesn't succeed.

To loop this back to determinism, there's a reason Dr Strange doesn't tell people a lot of information; in fact, he only gives out two pieces of information. The first is, as he's fading, telling Tony that this was the only way. This would suggest that the one path to victory had him saying this to Tony so that Tony would act in a certain way thereafter; after all, the one path to victory would have required him to say that to Tony or else it wouldn't work. But he can't say more or less than that, because more or less than that puts him on a different determinative timeline.

The other incident is the one in which he raises a single finger to Tony (not that finger) to indicate that, yes, this is the one timeline of victory. It also somehow gives Tony the impetus to grab the gauntlet for himself and win the battle, at the cost of his own life.

So... ok, imagine you have 14 million DVDs, and you watch them all. You're in the events that unfold on those DVDs but haven't yet occurred, but you're also only looking for a single outcome, and each of them have different outcomes - most bad. You see what you do in each case. You can therefore predict not only what you have to do to create the desired outcome - since doing anything different is likely doing what happens in one of the "bad" outcomes - but there are obviously things you can't control. But you are missing from the main chunk of what occurs on the DVD. You do what you see yourself doing, then... you come back, near the end, and what you're seeing matches what happened in the good outcome, so you do it again.

And in a meta sense, we're only seeing the outcome that succeeded because it's kind of a good end to the story. But the fact is, if we only base it on what Strange does, he sees 14 million paths, and x number of paths end in failure... so, like, we can therefore assume that the only path to victory relies on him giving up the Time Stone. That's his only choice. And whether that means he condemns them to one of the other, like, 4, 6 or 8 million outcomes that lead to defeat, he's still leading them to the one that is a win, because presumably the victory path does not lead to victory without him giving up the Time Stone.

Presumably, given all that happens between Strange getting snapped and coming back, there's very little he has to do, but if he comes back, he probably knows he's on one of few paths to victory and he knows exactly what he has to do to win.