I don't believe National inaugurated 747 service until later in the year - October, I believe on the MIA-JFK route. And I think Continental may have inaugurated service with their 747 before United... Anybody know for sure?
I can only offer first delivery dates for those who got the aircraft by the end of 1970, but as each carrier probably took pretty much the same time to get the type into service, it's a good guide.
PA 12-Dec-69
TW 31-Dec-69
AA 28-Mar-70 leased from Pan Am
NW 30-Apr-70
CO 18-May-70
AA 18-Jun-70 own aircraft
UA 30-Jun-70
NA 08-Sep-70
DL 26-Sep-70
EA 26-Nov-70 leased from Pan Am
As the overseas carriers came out in the same database lookup, and as all (except JAL probably) ran their first 747 service to JFK, here are theirs as well.
LH 10-Mar-70
AF 20-Mar-70
JL 22-Apr-70
BA 22-Apr-70
AZ 13-May-70
IB 02-Oct-70
SN 19-Nov-70
EI 15-Dec-70