All it sees is a big blob of text, some of which can be structured to differentiate turns between "assistant", "user", "developer" and "system".

In theory you could attach metadata (with timestamps) to these turns, or include the timestamp in the text.

It does not affect much, other than giving the possibility for the model to make some inferences (eg. that previous message was on a different date, so its "today" is not the same "today" as in the latest message).

To chronologically fade away the importance of a conversation turn, you would need to either add more metadata (weak), progressively compact old turns (unreliable) or post-train a model to favor more recent areas of the context.

LLMs certainly don't experience time like we do. They live in a uni-dimensional world that consists of a series of tokens (though it gets more nuanced if you account for multi-modal or diffusion models). They pick up some sense of ordering from their training data, such as "disregard my previous instruction," but it's not something they necessarily understand intuitively. Fundamentally, they're just following whatever patterns happen to be in their training data.