Some Protestants would argue that those with the Holy Spirit simply know what the canon is. I’m honestly not sure how popular this position is anymore, given how many holes it has. I only know of it through historical reference and haven’t read a modern apologist that I recall making the case.
Some Protestants are willing to embrace the idea that the canon is a fallible teaching, but they would still call it inerrant. They would say the same about, for instance, the Nicene Creed. Personally, I’ve really only encountered this in Reformed circles. It also may not be that old, given that it seems to be an invention of R.C. Sproul or one of his mentors, though I could be wrong in that regard. Either way, this one at least maintains the separation between infallible Scripture and fallible doctrine that Protestants maintain, but it does still leave open the question about why the canon is the one doctrine allowed to avoid being grounded in Scripture, which is something else Protestants otherwise require.
A final explanation is that since God, in Scripture, promised to preserve His word, then the canon is infallible, since it is the fulfillment of that promise. If I were to wager a guess based on my experience growing up and talking with Protestants after conversion, this is probably the most common explanation. This has the advantage in that it makes the canon grounded in Scripture, fulfilling that requirement, but it still leaves open accusations of circular reasoning, questions on whether or not God simply used His already-established source of infallible teaching to accomplish that promise, and questions on why God left us with a bad canon for 1400+ years (starting with the end of the New Testament around the end of the first century).
Ultimately, I think it is unfair to say Protestants don’t have an explanation. It isn’t like Protestant apologists are ignoring the issue entirely. Heck, it isn’t even always taught in apologetic senses. I originally heard explanations for the canon outside of any apologetic context.
With that said, I do think it is fair to say that there aren’t any good explanations. IIRC, Scott Hahn in his book Rome Sweet Home hints that he was so shocked by how bad the second explanation was that it was the final push he needed to commit to becoming Catholic.