Two days is still very early. When someone self-surrenders to a federal or state facility, there is an Admissions and Orientation period that has to be completed before the inmate's information fully propagates through the system and before communication privileges are activated. That process typically takes anywhere from a week to ten days, depending on the facility's intake volume and scheduling.
The database not showing him yet is normal for this timeframe. Systems update on their own schedule and newly arrived inmates often do not appear in public inmate locators immediately. Give it a few more days and check again.
Once orientation is complete, phone access, visitation, and commissary will open up. You can start getting money on his books through the facility's approved deposit method as soon as his inmate ID number is confirmed in the system. Sending a letter now is worth doing even before he shows up in the search, since mail can reach him during the orientation period even when other privileges have not activated yet.
He is in there and being processed. The silence is frustrating but it is the standard experience in the first week.