That was my impression as well. The first dossier filing was date 20 June 2016 and turned in to Fusion GPS. There are sources that say Steele met with one or more FBI agent in Rome in early July. I'm not sure how believable they are.
The spying on Trump's campaign (mainly to promote the Russia meddling meme) officially began at the end of July, but they were doing some of the setup work earlier, see https://www.steynonline.com/8667/tinker-tailor-clapper-carter-downer-halper-spy maybe as early as March 2016.
It's possible that CWB is essentially correct, that the dossier was the official paperwork for opening up operation Crossfire Hurricane. I may need to retract my previous post to CWB on this thread.
Mifsud ran a honey trap on Pop in March 2016. Victoria Toensing detailed it on Hannity this week.