OK, so the adventure includes not one but two abandoned wagon encounters. There's the one that Pral and his gang looted on the wilderness trail, and there's the one that Oleira is expecting that's running late because its driver got eaten by a stowaway ooze. The latter has some quirks.
I'm thinking I will combine the two for my opening scene.
Here's the background: Mallyn isn't just a random traveler; she does odd jobs around the Keep, including driving a wagon back to the civilized lands to the west to purchase supplies for Keep residents (mainly her Uncle Umbrusk and the trader Oleira). During her most recent supply run, a member of Ivlis' chaos cult hid a sealed jar containing a gray ooze glob amongst Mallyn's cargo.
The cultist may have been trying to smuggle the ooze to Ivlis via the Keep, or else they were hoping the ooze would get free in the Keep itself to cause some chaos there. It doesn't really matter because the PCs likely won't ever find out.
Unfortunately, Pral and his bandits waylaid Mallyn's wagon not far from the Keep. Pral politely had Mallyn stand aside while his men unhitched her horses so they could use them to carry the cargo back to their wilderness lair. However, as his men moved a crate, it knocked over the jar, breaking it and releasing the ooze. The ooze lashed out at a bandit. The bandit screamed, spooking the horses, which bolted. Pral and his gang fled too without really bothering to take any of the cargo.
Mallyn has been lurking in the bushes nearby ever since, too afraid to approach the wagon. When she hears movement on the trail, she worries that it's Pral and the gang returning, but when she sees it's the PCs, she makes her presence known and tells them her tale, perhaps embellishing it a bit since she's a lover of good stories. (She'll tell them that she saw a "slimy gray limb lash out at a bandit from within the wagon, striking him in the face and causing him to scream like he'd been burned.")
She offers to pay the PCs 12 gp (the amount the bandits left behind in the abandoned wagon encounter) if they can kill or drive off the monster and then help her get the wagon and its cargo to the Keep. She'll also tell them that she's sure her uncle and the keep's trader will both be grateful for their help.
After the PCs deal with the ooze, they can track the horses if they want to - I think a simple DC 10 Survival check to follow the horse's tracks will suffice. None of the characters are proficient in Survival, but the wizard has +2 and the cleric has +3, so that should be fine. They can work together, and the cleric can roll with Advantage. If they find the horses, they can then make a DC 10 Animal Handling check to entice them back to the wagon. (The fighter is proficient in Animal Handling but only has a +1; while the wizard and cleric still have their respective +2 and +3.)
When they get to the keep, Oleira will pay them 5 gp each to unload the wagon for her. I can have Mallyn take them to meet her uncle at the tavern, who will give them all a free drink or something as a thank you.
I'm also thinking that rather than waiting for the PCs to decide to visit the Castellan themselves, I'll have him summon them for an audience after they've helped ~3 Keep residents. He'll tell them he's heard of their good deeds and will then give them the Caves of Chaos quest and suggest they speak to his assistants for more quests.
As an aside, I note that the Keep booklet refers to Castellan Winvarle as an elf, but his NPC card lists him as a human. He doesn't appear to have pointy ears in his portrait, so I'm inclined to go with the latter. I'm also going to specify that his adviser, Elandra, is a drow elf. Her gray skin and white hair are a dead giveaway, but I guess they didn't make that distinction in the adventure so as not to confuse new players.