I found a way to reach Farore without the use of the Roc's Feather or the Ocarina, all at the start of a freshly created save file!. It utilizes 4 potions but is RNG heavy in multiple instances. I'll be adding it to the sheet, but it was worth noting that theoretically this is possible from the get-go.

This also means that ALL ITEMS in the start of the game are open for grabs from the start of the game utilizing only one potion (except the <s>Deku Leaf</s>), and you start with that free potion.

I've tested the game and you get roughly 100 Rupees at the start of the game just from starting the tutorial and getting the secrets. From there, if your RNG is good enough, you'll have 2 potions either Red or Blue in Syrup's shop, making the last potion more flexible in price. The only downside is that this RNG in potion prices has a second RNG: The potion effects.

Potions can explode dealing damage to you, and depending on how close you are affects how much damage you take. Ideally, you don't want to take any, which is where Healing, Magic shield, and Restoration come in to play. All 3 of these do 0 damage to you when blowing up, and the rest being negative in some capacity (Iron skin does up to 6 damage, Poison is poison, and Paralyze does 0, but you can't move).

I'll fix this up more, but I wanted it to be noted that this is 100% a possibility from the start of a fresh deleted game and was a nice find.