My understanding is the opposite. The entire process results in a "score" over all output tokens, which is then converted into a probability of being picked, using a softmax that takes a temperature as a parameter. With a temperature of zero, the "best" token is always picked, but interestingly enough, that does not give optimal results. So sometimes you want the second or even third best. Thus, a "good" (GPT-like) LLM is intrinsically random.
To put it differently: You can make them deterministic by using a temperature of zero (then the output would be pretty bad and repetitive), or having a "better" temperature and fixing a random seed (then the output would be better, but it would only be deterministic in the same sense as a simulation of Brownian motion with fixed random seed).
https://ai.stackexchange.com/questions/32477/what-is-the-tem...
Section 3.3 in https://www.lesswrong.com/posts/pHPmMGEMYefk9jLeh/llm-basics...
https://writings.stephenwolfram.com/2023/02/what-is-chatgpt-...