Not exactly. Page and JPJ were studio musicians, and of course Page was in the (New) Yardbirds, which also had Beck and Clapton at one time.
Clapton was also in John Mayall's Bluesbreakers, and was way more famous than Page. A fan wrote "Clapton is God" on the wall of an underground station, which pretty much summed it up. Bruce and Baker were part of the Graham Bond Organisation, which also had John Mclaughlin on guitar for a while.
Cream was together from 1966 to '68, and Zep didn't form until '68.
So Page followed Clapton to the Yardbirds, and I think it can be argued that Cream set the stage for loud rock bands that Zep continued.
Wikipedia sums it up thusly:
So without Cream, there might not have been a Zeppelin as we know it. Same can be said of the band Small Faces. Steve Marriott was very much the inspiration for the sound of Zeppelin, and they even wanted him in the band. Small Faces did the Willie Dixon song "You Need Lovin'" which is where Page got "Whole Lotta Love"
When Marriott heard Zep's version he said:
So looking at it from Jack Bruce's perspective, he was there first, and set he stage, and bands like Zep were followers, as well as contemporaries. But Cream was arguably the very first "Super group".
They are both great and important. Bruce could play circles around JPJ though.