Heavens yes, there are many ways to interpret the SOP. However, if not before the first flight of the day, perhaps the aircraft has flown without the inspection. To my thinking, it means - or should mean - before the first flight of the business day. And of course, one can quibble about that as well.
In the end, how many extra minutes do those checks require? Sometimes you know that they have been done; other times you
may not know a cold airplane from a semi-warm one. Your paxs' butts are on the line, as well as your crews' -and your own. It it about crossing the 'Ts, or checking the airplane again, to ensure a safe flight? Is a more thorough check worth your extra 5-10 minutes? I think it is, but your mileage may vary. You are already going to be a little late with push-back, so does the clock matter? I hope you DO make those few extra checks. They are worth your time.