I seem to recall that initially there was no engineering set built so Gene or someone scribbled in a scene in the pilot episode to justify getting it built. The story went that he was concerned if it wasn't built for the pilot it would never get built.
So they slapped together a set.
It does seem odd that the set changes half way through filming until you realize how the shooting schedule worked. They couldn't very well stop shooting for a construction change. Between one take and the next -- and no one will ever notice let alone discuss it obsessively decades later, right? Right.
...
As for all of the engineers the ship went through -- head-canon time. There were three Galaxy class ships in service with more planned... so they were rotating candidates through the existing ships for training. The Enterprise trained several candidates, Galaxy herself trained a few more and so on, so there was an engineer pool to draw from as the ships came online.
LaForge was one such candidate. He had the leg up on everyone else as Picard personally picked him as a staff member (there was a bit of backstory about that) so he got the prize posting while
MacDougal went on to Chief Engineer the USS Venture,
Argyle got the Odyssey
, Logan got the USS
Yamato and
Lynch got the Challenger. Again I have nothing to back that up that's head-canon.
The next block of ships the Galaxy Flight II and IIA models would prove to be much less combustible under expected operational conditions thanks to the logs of this first group of Chief Engineers.
"Engineering Log: Ensign Swiffberg sneezed in the general direction of the warp core, and we had to perform an emergency shutdown to repar the damage."
"Engineering Log: "Discovered that someone at the yard failed to understand what a "jettison-able hull plate for core ejection" is. Thankfully we noticed that BEFORE we had to eject the core."
"Engineering Log: "Lt. Muffslager sneezed in Engineering, catastrophic core damage nearly destroyed the ship."