Function that is guaranteed to be one-way if one-way functions exist? There is an old trick for writing down an algorithm that, if P = NP, solves SAT in polynomial time.  Essentially, one lists all polynomial time machines and multi-tasks over them.

Is there an analogous trick for one-way functions (or even one-way trapdoor functions)?  That is, can we write down a function that, if one-way functions exist, is necessarily a one-way function?

There seems to be no easy way to mimic the P = NP trick.  In that case, we can quickly recognize a solution when we get one.  But if I multi-task over all polynomial time functions, there's no obvious way to recognize a one-way function when I arrive at one.

If the answer to the above question is no, is there some kind of argument why we can't do it?  Maybe writing down such a function would somehow prove that one-way functions exist?
Yes, such a function was found by Levin himself, published somewhat recently:

The tale of one-way functions. Problems of Information Transmission (= Problemy Peredachi Informatsii), 39(1):92-103, 2003.