This has happened to me- once.
It drove my change in practice to ALWAYS making a starter. I even make a starter if I use a dry yeast pack.
At this point, my outlook on it is you can wait a while longer, but that has one big downside- the longer the wort waits to begin an active ferment, the greater the exposure to negative bacterial activity.
It sounds like the yeast pack you opened was weak, if not dead. It could take off in the next day.
When it happened to me, I tossed a dry yeast pack in and got it over with.
By comparison, when I started a fermentation yesterday, I pitched a liter of krausening yeast from a dry pack I had hydrated at 4 PM.
At 8 PM it had a 2" head on the batch. By bedtime it was blowing off the 6 gallon fermenter.
This morning it had overblown the blow-off a bit. I put some secondary containment under the blow-off. The clear 6 gallon fermenter is absolutely opaque in the krausen area.
I expect the primary to complete in 24-48 hours from 1.055
A couple weeks ago I had one finish from 1.095 in 48 hours.
I love my little yeast buddies!