"And with SpaceX only solving problems as they occur, how many runs will it take them to get it correct?"
A very valid point indeed. The answer is twofold.
On the one hand, SpaceX solves problems by moving fast and breaking things. I'm not being sarcastic here; that is their SOP. They're not afraid of blowing things up, as long as it provides data on what's borked and how to fix it. And it does. That, plus the amount of dosh Musk is able (and apparently happy) to throw at it allows them to move forward at a spectacular rate. Don't get me wrong: I am most emphathically not a fan of the Elongated Muskrat. However, I must point out that SpaceX has achieved more in less time than any governmental space agency or any other commercial company in the field ever has. So there is no doubt in my mind that they will be able to deliver the techology.
Eventually.
Because the other side of the coin is that they're literally making it up as they go along. That's fine; it obviously works for them, but it also makes it impossible to deliver on schedule, because the schedule is just based on when they last had a RUD, how many so far, and how bad it was.
So while I'm certain they will eventually reach the point where they pull off a lunar landing, I'm sure they will eventually pull it off somehow.
Will they deliver in time for NASA's moon landing schedule, though? That, I believe, I can reliably predict: No F...'ing Way. Forget it. SpaceX states that Starship Block 3 may fly this year (read: with luck we're looking at sometime in Q1/2026) and when Block IV will start test flights nobody knows, because that all depends on how many Block III RUDs they'll have before they get it right.
I can't see Starship being certified for human flight before, oh, 2028 or '29, if that. Apart from that there's a tonne of other problems still to be solved, not the least of which is the orital fuel transfer, since nobody has any clue what the actuall the boil-off rate of liquid CH4 and LOX in space will be.
So a mid 2027 manned Lunar landing is clearly not going to happen, no matter how you look at it. As it currently stands, the entire Artemis timeline is a pipe dream.