What determines a new cryptocurrency's initial value?
A cryptocurrency's initial value is set at the same way as an established cryptocurrency.

It's the price that people are willing to pay, when they believe the hype told to them by the crypto's promoters.

As such, the price is a measure of the promoters' marketing skills, and the gullibility of the buyers.

I completely understand that you feel it ought to be different. But for an intrinsically worthless thing, what I've written above, applies both to a new crypto and an existing one. It's worthless. Therefore its price is whatever the owner can fool someone into paying for it.

As for what number the promoters actually pick, they will play a guessing game. There's a story about how opticians price the pair of a new glasses. When they tell a new customer the price, they say, it will be £60. And they pause, and watch the customer's reaction. If they don't blink, they add "per lens". Pause, and if no blink again, "and £120 for the frame". If the customer looks scared, they can then add "but with your discount, the frame will be half price".

Pricing worthless assets is similar, but far worse. The seller make a pretty fairy story about the total value of the market, works out how many tokens there will be, throws in a big "get in at the ground floor" discount, and then plucks the asking price out of thin air.