I bought the Lotus Field Pioneer precon. It’s billed as being able to win in a single big turn, and the apparent way to do this is Granted, Omniscience, a second Granted, Approach of the Second Sun, Dig Through Time, and a second casting of Approach. But this requires two Lotus in play and either 3×Hidden Strings and 1×Granted, or 2×Hidden Strings and 2×Granted, plus Dig Through Time in hand, which seems like a tall order. What am I missing here about how this deck (in its natural state, no Ultimatums) wins in a single turn?
You aren't missing anything. That's how you win. See this old article.
So Step 1 is get to fourteen mana with a Fae of Wishes in hand and something to do with Omniscience. Eighteen mana with two extra dead cards in hand is "something to do with Omniscience" as well, since you can recast the Fae of Wishes, return it to your hand, and Granted from there for a win.
Getting to 14 mana is of course going to be difficult, but remember you start netting mana once you have two Lotus Fields in play (and Thespian's Stage is also Lotus Field, that's why it's in your deck). It's more than just Hidden Strings as well - Pore Over the Pages also untaps lands (thereby netting mana), and so does Vizier of Tumbling Sands.
If you do reach 18 mana you can also Granted -> Omniscience -> [Hidden Strings / Pore Over the Pages / Vizier] -> Granted -> Peer into the Abyss (if you aren't at 1 life) which gives you more Hidden Strings / Pore / Vizier, plus card draw -> Granted -> Approach.
And finally yeah, the preconstructed decks are never going to be top-tier. You'll want to upgrade (with Ultimatums).