How can he justify the belief that beliefs are justified by sense-experience without first assuming his conclusion?

I don't know what exactly "justify" is supposed to mean, but I'll interpret it as "show to be useful for helping me win." In that case, it's simply that certain types of sense-experience seem to have been a reliable guide for my actions in the past, for helping me win. That's all.

To think of it in terms of assumptions and conclusions is to stay in the world of true/false or justified/unjustified, where we can only go in circles because we are putting the cart before the horse. The verbal concepts of "true" and "justified" probably originated as a way to help people win, not as ends to be pursued for their own sake. But since they were almost always correlated with winning, they became ends pursued for their own sake - essential ones! In the end, if you dissolve "truth" it just ends up meaning something like "seemingly reliable guidepost for my actions."