Yes, at least theoretically. An example of how this might be is given in the first of Descartes' Meditations on First Philosophy. Descartes asks us to consider a world that is governed by a kind of evil god who delights in nothing more than making us believe what is false. In such a world, we would be able to find no evidence at all to debunk the falsehoods to which the god inclined us. Descartes challenges us to see if we can be absolutely sure that we do not actually inhabit such a world!

Modern popular culture has taken up this scenario in various entertaining ways. I think it is fair to say that the worlds imagined in "Total Recall," and "The Matrix" are excellent examples of scenarios that raise the theoretical possibility of false belief that is (at least for those who don't escape the Matrix!) invulnerable to refutation.