What determines a new cryptocurrency's initial value? I understand that a cryptocurrency has no intrinisc value, and that therefore its value is determined strictly by market forces, i.e. supply and demand.

I "get" (more or less) that this is how it works for cryptocurrencies that are already "up and running", but what I don't get is how a cryptocurrency's market gets started. I mean, there are over 800 cryptocurrencies already, with a couple dozen pretty well-known, right? So apparently starting one isn't very difficult. But when someone starts a cryptocurrency, how does his first (and his second, third, etc.) "coin" acquire any value in terms of traditional money? I mean, I understand that the first transaction gets the cryptocurrency's "market" going, but that transaction is internal to the currency, right? It does not establish a value relative to a traditional currency.

I also don't get who would enter into that first transaction anyway. If some person tells me "Hey I started a new cryptocurrency, so far I've mined 1 unit of it. Can I use it to buy a can of beer from you?", why would I ever say yes, given that there is no way to determine what is a reasonable "starting value" for his currency?

(I did read up on a bit ICO's, but I don't quite get that either. OK, some "company" proposes to create a bitcurrency, and investors can buy into it prior to its creation. Does that mean they buy a certain number of the yet-to-be-created currency? In that case, again I don't understand what possible basis there could be for assinging a specific 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.