Is it a "new" fuel pump? If so, they're all garbage straight out of the box. If it's an original pump or a replacement pump from 30 + years ago, have it rebuilt.
Then & Now rebuilt mine over 4000 miles ago and it works perfectly and is able to prime the carburetor without much effort.
If you don't have an old made in USA pump, look for one on ebay and rebuild it.
1950 Chevrolet 3100 (Ol' Roy)
1939 Packard Standard Eight Coupe (The Phantom) | 1956 Cadillac Coupe de Ville (The Bismarck) | 1964 Ford Galaxie 500 coupe |1966 Ford Mustang (Little Red) | 1969 Pontiac GTO (The Dishpit) I 1979 Ford F-100 | 1976 Ford F-150 (Big Red) | 1995 Ford F-150 (Newt)