You would probably be okay putting it up early, but I am always reluctant to do that. I would probably gamble that putting it up right after that first egg would still beat any HOSP attack.
If, however, the HOSP is showing interest in the box like sitting on top and yelling for a mate to “come see”, I have found the fastest and simplest way to tell him “No” is with a Van Ert Universal Sparrow Trap. This is faster and addresses the specific offending HOSP better than my revolving door trap. The male is known to find a site and call for a female. But while he waits he goes in and out. That’s when the door goes shut and his story is over.
Cari
Willamette Valley, Oregon