I don't have any earlieer usages to report, but your suggestion makes sense. The legend is that someone (an Alco employee?) had chalked "Big Boy" on the smoke box (?) of the first (?) U.P. 4000 off the production floor at Schenectady, and that this name stuck. But there's no reason to think that the man with the chalk intended to give a NAME to the type: he was just DESCRIBING the new gargantuan, using a common expression, "Big Boy," that has been used with reference to many impressively big things, not all of them locomotives.
(If it hadn't stuck, what would we call the 4-8-8-4 type? Double Mastodon?)