Delta does not make pre-boarding announcements. They will allow people to pre-board if they need to (e.g., disabled), but I wouldn't count on it to just carry on a car seat. Why do you feel that you need to pre-board? It's not that hard to board with kids along with everyone else; I've done it plenty of times.

Ask for a bulkhead seat at check-in if you would prefer to sit there. Gate check the stroller (no need to store it in the plane since you can't use it).