The concept of "signposting language" is not just any word or words that help guide the listener (most words will do that to some degree or other). "Signposting language" is language that is inserted primarily for that purpose and does not add any particular meaning or information of its own beyond that.
The phrase "the first time" actually does have important meaning in the sentence. It is not there just to guide the listener. If we remove it, we get basically:
Have you (not) had a problem like this?
But this could be interpreted as asking "have you had a problem like this for a while?", and since Alice has been having these headaches for a week, she might answer "yes, I had this problem every day this week." However, "the first time" indicates that the doctor is asking about distinct episodes (times), and is therefore asking whether she's had this problem before this current time, which is an important distinction.
Another way to ask the original question might be:
Have you had a problem like this before?
But again, "before" here is needed to make it clear that the doctor is asking about times before the current incident, not the current situation (so it is also not just there for signposting).
Note that your other examples of "sign words" are also generally not "signposting language" either: "never" adds information that the speaker is explicitly talking about something "over all time" instead of just recently, for example. "for" is a general-purpose preposition that can have many important meanings in different contexts (and usually can't be left out without changing the meaning of the sentence). "since" implies a causal relationship between one thing and another, which is usually important information, etc.
Many of these phrases are also useful for directing the flow and comprehension of the language, but that is not their primary purpose, and they have other important functions beyond just that, which is the important distinction.
"Signposting" in general doesn't actually happen that much in normal conversation. It is something that is often used in more formal contexts such as academic or professional writing, or when making presentations to lots of people, etc. The reason for this is because in those situations, the author/speaker is presenting to an audience which is not able to give them a lot of feedback regarding whether they have followed the language correctly or not, so they want to put in additional words to make extra sure that people can easily follow it. In one-on-one conversations, there is a lot of feedback already, and it's easy for one person to figure out if what they said was misunderstood and restate it another way if necessary, so signposting is not usually necessary.
