I agree with the DL"s translation : I think my moment has come. However, I have a problem with understanding the inversion of the dependent sentence. Penso che sia arrivato il mio momento. As clearly seen after che the compund verbs ( sia arrivato) of the dependent sentence appear first before the subject of the sentence ( il mio momento).
I would like to know why such an inversion is made and why it is needed.
wait ... I didn't get why you have told it's creepy. I had to stop and read again. Beware that this sentence in Italian is an optimistic cliché. Tomorrow you will meet a customer and maybe, maybe, this guy will make a 100 million USD order. And you tell your wife : è arrivato il mio momento. And you add: Gli farò vedere chi sono. I'll show them who I am, the best **ing salesman of this business !!!
Put in google "è arrivato il mio momento" and see how they are all optimistic situations.