I’d do as Mema said and make them in advance.
We had a GS in September 21. Never got a welcome email from the concierge so just showed up after to boarding to make dinner reservations. We were only offered a couple of reservations at 8:30 for dinner which I didn’t want so just left with no reservations.
Later that night we were tracked down while we were in Central Park by someone from CK asking us what day and times did we want dinner reservations. I didn’t get the impression we could get all nights. We’re not the type to beg or pressure for good service. I didn’t want any reservations at that point but just threw out a night and he pulled us into a closed CP 150 and made our reservation.