I'm not going to do the math on this, and there may be more optimal configurations, but here's the basic idea:
Dance of the Manse
Go second. Skip the first land play, and discard Thousand-Year Storm (TYS)
Play 2 Islands
Play Lotus Field, saccing the two Islands
Play 2 land each turn. Upon playing your 7th land, play Nyxbloom Ancient (NBA).
Turn 9: Play a 6th land (8th land drop, minus Lotus Field sacs)
Tap Lotus Field for 9 W, 1 island for 3 U
Cast Dance of the Manse with X=6, returning TYS to the battlefield as a creature (2W2U remaining)
Cast Quasiduplicate (QD), targeting TYS. TYS copies QD, the copy targets NBA.
Let the copy resolve, then tap an island for 9 U (1W9U remaining)
Cast Narset's Reversal* (NR) on QD. The two copies of NR both target NR. The first will bounce it, and the second will fissile. The copy of QD created by the copy of NR will create a copy of TYS.
Cast QD again, this time getting 6 copies. Then cast NR, getting 8 copies which all target NR.
I think you can see where this is going. For 5 mana, you get to play Quasiduplicate with Buyback, and tick up your storm counter twice. This is not an infinite combo, because you can only get mana from your lands, and each land can only be tapped once. But each land generates a ton of mana (3^N, where N is the number of Nyxbloom Ancients in play).
You can repeat this every turn until you run out of cards in your deck (see, still not infinite). At the very end, tap your Lotus Field for ungodly gobs of mana.
*For our purposes, when Narset's Reversal creates a copy of a spell, that copy will always target the original target. There's no benefit to switching targets, so I'm not going to bother to mention it in the main description.
Possible Deck Adjustments
I'm not sure what the optimal ratio of Nyxbloom Ancients to Thousand-Year Storms is for targeting with Quasiduplicate is. It's possible that Nyxbloom Ancient is always the better target, in which case you can drop Dance of the Manse entirely and replace it with a 55th land. I'm pretty sure that that isn't the case, though.
There will be 2 (or 3 if you drop Dance of the Manse) islands left in your hand at the end of the game when you deck yourself. You can replace those with Firemind Vessels (which will speed up your engine a turn, and give you more mana on the board), but this is a bit of a tricky point in the rules of the challenge, since if you discard a Vessel the way you discarded the Thousand-Year Storm and then reanimate both of them, the deck goes infinite. Does it disqualify a deck if the deck is capable of going infinite even if you play it in such a way that you never reach that capability?
Obviously, if you cut Dance of the Manse (as mentioned in the first possible adjustment), then the Vessels are safe to include.
You can also replace one of the islands with Dryad of the Ilysian Grove, which will let you play the other island a turn early.
Another possible substitute for the last land is Repeated Reverberation, which combines with Narset's Reversal to be two Quasiduplicates for the cost of [3RRUU]. This is a better rate than 1 QD for 1UUUU, but it means you have to juggle your mana sources between R and U, and each land can only tap for 1 color at a time (even if its a multicolored land, the tripling will copy the color being produced), so I'm not sure it actually works out as more effective.
You can also include a mana dork (such as Paradise Druid as the last card. These can be copied by Quasiduplicate, but because they don't have haste they can't be used for mana the turn you create them and you still don't go infinite. I'm pretty sure that you're better off copying Nyxbloom Ancient over a dork every time, though.
Wilderness Reclamation may also be a valuable addition when combined with Teferi, Time Raveler to give Quasiduplicate flash. You're effectively doubling the number of lands you have, and if you Dance of the Manse it you can start ratcheting up that multiplicative factor. This isn't an infinite combo because the untap triggers only happen once per turn, but I'm still not sure if the extra untaps are worth giving up copying Nyxbloom Ancient (My gut says yes, but you also lose a turn to pitching Wilderness Reclamation into the graveyard, so it's hard to judge).