If cryptocurrencies have no intrinsic value, how do they originate? In theory, anyone could create an infinite quantity of their own cryptocurrency right now. However, if you were to do this, it would have no value and, thus, it would be useless. 

Since value comes from demand, how is it possible to create something from nothing and expect people to pay for it?
You seem to have a misunderstanding:


  anyone could create an infinite quantity of their own cryptocurrency right now


This is not accurate.  The breakthrough that enabled Bitcoin (and other cryptocurrencies) was the ability to make a digital asset scarce without trusting a central authority.

In the past, currencies (digital and otherwise) have required an issuing party, whom we all have to trust won't hyperinflate the currency by creating too much of it.  This might be a regional bank, a central bank, a government, or something of the sort.  Bitcoin changed this.  By using a few clever cryptographic tricks and some game theory, Bitcoin is able to give its users a very strong assurance that hyperinflation will not occur, without anyone trusting a central authority.  Bitcoin has decentralized digital scarcity.

What this means, is that there is a fixed supply (which nobody can reasonably increase) of a currency with a built in transaction network.  There is plenty of demand for such a system, yet limited supply...therefore, there is value.