Of course he has a team and I believe protocol is that first person who is contacted by “NORAD” when a launch is detected by satellite is either the Secretary of Defense or the Head of the Joint Chiefs. They will then connect immediately to the White House - probably the Chief of Staff to the POTUS.
But it’s a short window of time to react. Something like 6 minutes for a ground to ground launch. Less time if it is a sub launch. The decision whether to counter-strike is up to POTUS but hopefully nobody is dumb enough to initiate a full scale nuclear holocaust on the earth. If there is only one launch, there may be a decision not to escalate.
Well I hope the president will be able to find the SOD. After all he was in hospital for a week before Biden knew it.Austins replacement was at the time on vacation.