As can be seen in the below image of Archer's ready room, there are four sketches of various ships bearing the name Enterprise:
Compare this, though, to to the below image seen on the Enterprise in Star Trek: The Motion Picture:
Now, the first three images in both pictures above are of the same ships. Then we get into interesting territory.
The Enterprise NX-01 isn't shown in the picture aboard the Enterprise refit from TMP. That's understandable out-of-universe, because Enterprise hadn't been made by the time they made TMP.
Yet, there is a ship between the Space Shuttle Enterprise and Star Trek's USS Enterprise on the Enterprise in TMP. I've found out that this ship is the USS Enterprise XCV 330 which, according to Memory Alpha, was in service prior to 2143, something established in Enterprise: 'First Flight'. The series Enterprise starts in 2151 according to Memory Alpha.
So, it's made pretty clear that the XCV 330 existed prior to the NX-01. We also know it was significant enough to be put on a display gallery on the refit Enterprise in TMP.
So, why is the Enterprise XCV 330 not on the wall in Archer's ready room?