If you accept that "the first time through" Cochrane accomplished his first warp flight without the assistance of the Enterprise crew, and without having the majority of his ground crew killed by the Borg, then sure, First Contact definitely represents a change in the timeline.
I think that the reason we didn't see the supposedly extremely important
NX-01 on the Enterprise Dee's observation lounge wall was because originally none of the NX's were named Enterprise. The NX-01 was named Enterprise in the alternate timeline because Deanna told Cochrane the name of the ship in orbit that Cochrane saw through the telescope. Cochrane later request that the "warp five ship" be named Enterprise.
I was recently thinking about this. The NX-01 wasn't named Enterprise in the unaltered timeline, but after Cochrane interacted with the ENT-E crew and Deanna named dropped their ship. Cochrane who worked on the NX project probably pushed for the NX-01 to be called Enterprise.
If ENT was in a different timeline caused by the Ent E's interference, wouldn't Picard and Co have returned to that alternate timeline and noticed the difference?
"Hey, what's this about the NX-01 being called the Enterprise? *Oh, right. *I guess Temporal Investigations will be visiting us soon..."
See my question number 4 below. But yes the effects of the Borg and FC would leave the ENT-E with the only complete, unaltered history logs prior to the incursion, the scans and visual recording of Borg assimilated Earth 2063-2373, and what all the ENT-E crew did while in the year 2063. We can be sure when delivering their reports to Starfleet, the Temporal Investigations branch was also there to shake down the crew for info about what happened and changed. Similar to what they did in DS9 Trials and Tirbblations with Sisko.
As for the Borg and unaltered timeline. I posted recently in another thread about their effect on history. I'll copy and paste here
What happens in First Contact is the Borg travel back to 2063 Earth and rewrite history in their own image. We the audience and the crew of the ENT-E saw this from the 24th century. Because the ENT-E was displaced temporally by the wake they were in they existed outside of time and were shielded from the effects. The was no first contact and the Federation and Star Fleet never existed.
Unaltered Timeline: 2063-TOS-TUC-TNG-DS9-GEN-VOY-2373 :Erased by Borg's Time Incursion to the past
Borg Timeline of Earth 2063-2373 now established.
The ENT-E crew went back to CORRECT what had been corrupted, and they succeeded. However they failed to prevent several people from dying and had to contaminate the time stream and give assistance and future knowledge to Zefram Cochrane and Lily Sloane. Not to trivialize these details but what was PARAMOUNT about this was ensuring Earth and the Vulcans made contact. This was the broad stokes of history that NEEDED to happen in order to ensure the Federations future.
New timeline: 2063(altered)-ENT-Regeneration-TOS-TUC-TNG-DS9-GEN-VOY-2373(altered).
However this is where the predestination/pogo paradox gets thrown around and it's incorrect. In VOY Year of Hell part 1 7 of 9 states the Borg were present at the events of First Contact. In VOY Relativity she states that the Borg traveled back in time where they SUCEEDED in conquering Earth, but that led the Enterprise following them back and changing the course of events. To which Temporal Star Fleet guy says "in a way the Federation owes it's existence to the Borg". Temporal Starfleet guy.. You're fired.
Had the Borg never traveled back to stop Cochrane the flght would've been a success regardless and the Federation would've been founded.
Relativity and Year of Hell part 1 where Seven brings up the Borg and FC are goofs on the sides of the writers. They were trying to be clever and witty but overlooked what was actually shown in FC. Ask yourself this:
1. How does Seven know the Borg succeeded? If Earth was assimilated in 2063 through 2373 then how does any record of that remain in the revived timeline where the Borg were defeated by the ENT-E?
2. Same question, How does Seven know the Borg succeeded? It can't be a predestination/pogo paradox that the Borg would both succeed in their goals (assimilating Earth 2063-2373) and fail at them in the same span of time 2063-2373.
3. Since the Borg never sent the message to the Delta Quad, thanks to Picard and Worf blowing up the disk. The DQ Borg had no knowledge there were Borg on Earth.
4. The ENT-E crew had the historical logs and the time frame of events of what should've happened down to the letter. The basically steered history back on track. However several people did die and Cocharane, Lily and their colleagues had all seen or at least interacted with the ENT-E crew. All of this is bound to leave impressions and change history.
There was only one timeline which kept getting changed by different parties. We see a similar event occur during ENT with the Xindi Sphere Builders and other Temporal Cold War factions. Everyone trying to supplant the past that exists in order to rewrite the future in their favor.