There are honestly too many variables to give a good prediction. A party that is single-mindedly dedicated to it (and lucky) may find it in the first day. But I think 6 days are enough for most parties to either find it, or find the ingredients to make their own.
To give an example of how unpredictable it is though, in one of our playtests neither the party nor the Heir found the antidote because they ended up killing the Heir in a case of mistaken identity, trying and failing to ally with the goblins, then went to Watchtower Without Wizard to cut loose the tether and leave the Keep (and their many pursuers) with their heads still attached to their necks!