Since this stuff gets rewritten as we go, what about the Bonaventure from TAS’ “The Time Trap”?
Going by the strict dialogue, Bonaventure should be older than NX-01, not newer. Bonaventure was the "first ship to have warp drive installed".
I take TAS with more than just a grain of salt. Alot of it just flat out doesn't work in the slightest, and was officially not canon for decades. However with the Bonaventure, in my own working out of the Trek chronology, I assumed it was the first true "starship" to have warp drive, in the last 21st century. The Phoenix and the probes and what not had warp drive, but Bonaventure was the first ship with a crew set out to explore.
For that theory to work, it has to be prior to 2069, when Conestoga was launched. I tend to ignore any visuals from TAS, so i'm seeing Bonaventure as a small vessel cobbled together somewhere around 2067 just a few years after the Phoenix flight, probably with some help from the Vulcans. While the Vulcans were trying to keep Earth contained, a diddly little vessel flying around at Warp 1 wasn't really going to have the range to do much of anything, and gives the humans something to rally around.
EDIT -
Just wanted to pop this in here as we talk about the Daedalus. I've put alot of thought into post-ENT era and have a whole slew of theories/headcanons. One such is the origins of "NCC". In my version of events, the Daedalus is actually based on a somewhat older design that never actually made its way into production, designed as a military ship by a now-defunct Earth military (I have it pegged as US Space Force). Starfleet pulled the design out of mothballs, needing something designed for military operations and realized it was an easy ship to build.
(trying to reconcile "old" canon with new), the initial purpose of the Daedalus was essentially as a mobile missile platform. Given they needed huge amounts of ordnance, Earth was unable to manufacture photonic torpedoes at that scale and fitted these vessels with massive amount of old-style nuclear warheads. Being wartime and nobody wanting to get creative with naming, this design was given the simple name of "Nuclear Combat Cruiser", the first to roll of the line being NCC-10 Daedalus. (Mirroring what someone said earlier, the Sphere is the habitation area, the secondary "tube" is mostly taken up as munitions storage/missile launchers)
Much like the NX-Class, the NCC-Class didn't have an official "name" other than its letter designation. At the end of the war, the refit NX-Class became known as "Columbia-Class" after NX-02, the first to receive the refit, and the NCC-Class was dubbed "Daedalus-Class", starting a tradition that would last for centuries.
It was the NCC/Daedalus-Class that projected Earth from minor power to the most powerful fleet in the quadrant, and upon the formation of the Federation, most Starfleet ships would be given a registry beginning with "NCC" in honor of the now-legendary class of starship. (The NX-Class, of course, would also be remembered and honored with experimental or one-of-a-kind vessels receiving the "NX" registry.)