Question Regarding Grammar Points with を X に Format

I’m going through the more intermediate/advanced grammar points right about now and have come across a few with a similar structure that uses を and に (を中心に、を契機に、をきかっけに etc). I’m a bit confused by these expressions because of the を particle; until now, I assumed を was used to mark the direct object of the main verb of the clause, but the を here seems to serve as a direct object marker for the expression/phrase that comes directly after it (中心、契機).

I noticed, however, that in the alternatives shown for をきかっけに, you could say something like, をきっかけにして or がきっかけとなって. Based on these alternatives, I came to the conclusion that this expression involves an omitted verb for the sake of brevity. Am I correct in this assumption, or is there something else going on here? Thanks!