The short answer is that you should keep the house relatively cool, but maybe above your comfort level while you're not there, and well insulated. The details of when it's best to run the AC for maximum efficiency pales in comparison.

The AC will be more efficient in the morning, for one, than during the heat of the day. And if you let the entire house get truly hot inside, it will take a lot longer than 30 minutes to bring the temperature down (it's not just air that has to get cool, it's all the solid objects as well). And when it's fairly hot outside, it may not actually be possible to get it cooled down if you wait until the heat of the day. E.g. my AC will keep my house at 70F when the temperature outside is over 110F, but if I let it drift up to 80F inside and then try to bring it down to 70F in the mid-afternoon, it won't get any lower than maybe 75F until the ambient temperature outside drops into the 90s.

The same effect works in reverse though, maintaining temperature through the heat of the day is wasteful if the temperature drops before you get home. If you’re dealing with significant solar gain then running a fan before turning on the AC becomes even more efficient.

Only if it's already cooler outside than inside the house. On a day where it's only 90 out during the day, it's not dropping to 75 until 8-9pm at the earliest.

Also can't use a fan on the west coast in the later parts of the summer when the air is full of wildfire smoke.

An example of significant solar gain would be a car sitting outside in sunlight. A surprising amount of modern architecture would work just fine as a greenhouse. Assuming a 9 hour workday it’s going to get well above ambient before you get home.

I could not find the example problem I was referencing in my textbook, consider me either incorrect or ambiguous until I do. I'm going to look through my notes next. I believe it was a problem from my professor.

I remember this problem being absurd, like bigger than a mansion.

Gosh I wish I could find it. I've referenced this problem a few times, I need to find it. I might have the book, if I can find it I'll update this post.