Do Germans understand the word "Inbetriebnahme" to simply mean getting a system up and running at any point, or does it specifically mean getting a system up and running for the first time only?
Without context, Inbetriebnahme would mostly be understood as the initial installation and first startup of a rather complex machine (industry machine, robot, computer, car), like jera points out in his/her answer already.
However, in a legal context or in a sophisticated text, like a DIN or a police report, or a law text or court proceedings, or a user manual, it may also mean the act of powering up and starting to use a machine or mechanism in the broadest sense (industrial machine, car, computer, hair dryer, swing set on a playground), regardless of whether it would be the first, hundreth, millionth or last time.
This is why Duden gives two meanings for the word.
In day to day conversations, it'll not be clear as to which one is meant without context, so one might pin down the intended meaning by supplementing the usage of the term:
Ich habe gestern mal wieder meinen Lego-Roboter in Betrieb genommen.
(Deconstructs Inbetriebnahme to in Betrieb genommen.) Here, mal wieder (once again) is used to point out that this has happened before, but that it's not important when exactly this took place.
Fritz nimmt morgen an der erstmaligen Inbetriebnahme des Riesenrads teil.
Erstmalig is used to emphasize the novelty of the act.
Meine Mutter wurde gestern Nacht zum letzten Mal bei der Inbetriebnahme ihres alten Staubsaugers gestört, denn morgen schenke ich ihr einen geräuschlosen.
Zum letzten Mal as indicator for repeated start-up, but narrowing it down to the last time ever.
focus of "Inbetriebnahme" is something initial, not very light-weight.
- "Nach Inbetriebnahme des Druckers ..." ~ "after setting up the printer"
- "Nach Einschalten des Drucker" ~ "after powering on the printer"
E.g. "repair and setting up the printer" would be "Wiederinbetriebnahme"
According to the machinery directive, the Inbetriebnahme is the initial commissioning of a machine.
Depending on the sentence you use it in, most of the time Inbetriebnahme would be understood as the initial commissioning and not as an everyday start-up of a machine.
If you are looking for a word describing the start-up it would rather be