To the OP, first off, congratulations on the offer! I would not bring it up unless coaches ask, or your son has other interest (where he would more like to attend), and the offer has a tight time frame. In the recruiting process often coaches would ask, "who else is interested." Son would be more hesitant here, but name a couple of schools that he did have most communication (both his and theirs). You do want to be honest. In most cases the coaches had some idea, as son's focus was primarily on schools in D1 HA Conferences.
That initial offer can help, especially if it with a strong baseball program. One morning/early afternoon, son went on an official visit at Big State U. He received an offer at the tail end of the visit. The school where son ended up committing, knew about the visit. Upon hearing of the offer, they also offered that night after his Legion DH.