As far as I am able to see, there are only two positions one can adopt in answer to this. They are: “truth exists” and “truth does not exist”. One cannot say “truth sometimes exists”, because that means that it does. Nor can one say “truth is subjective”, because there are otherwise no true standards by which we can measure its validity. Saying “maybe truth exists” is neither here nor there.
The problem with the question “does truth exist?” is that it can only be answered within a framework that assumes the existence of truth. If one says “truth exists”, what they are really saying is “truly, truth exists”, and when someone says “truth does not exist”, what they are really saying is “truly, truth does not exist”, or “truth has a truth-value of zero”, a contradiction not just of terms but of logic. If this point is answered by saying, “how do I know that logic is true?”, we can see that the disbeliever of truth has it all ahead of them: if one does not believe in truth, one does not believe in logic, and, of necessity, nothing can be believed. We must concede that truth exists if we are to do or think anything. The exact nature of this truth is another matter, but truth undoubtedly exists.