There's some statistical nuance here. LLMs output predicted probabilities of the next token, but no modern LLM predicts the next token by taking the highest probability (temperature = 0.0), but instead uses it as a sampling distribution (temperature = 1.0). Therefore, output will never be truly deterministic unless it somehow always predicts 1.0 for a given token in a sequence.

With the advancements in LLM posttraining, they have gotten better at assigning higher probabilities to a specific token which will make it less random, but it's still random.