(Spoilers, by the way)
It's basically impossible to do a sandbox for any adventure where there's a strong story involved. However, that doesn't mean that individual episodes of the adventures can't allow the players a variety of approaches (and the DM a variety of approaches in how to handle them). It doesn't change the fact that certain things have to happen to lead the characters onto the next episode, but it does mean that the adventure isn't 100% forced.
The first episode of Hoard of the Dragon is a good example of this style of design. Let's look at its structure:
Introduction: The players come to Greenest for a variety of reasons and discover it's under attack by a dragon, kobolds and humans.
Opportunities for Adventure: The DM presents the players with a number of adventure opportunities: The players see the cultists burning the mill. They encounter villagers needing escort to the keep. The dragon attacks the keep. The cultists attack the church which has villagers inside. A warrior of the cult challenges the defenders to send out a champion.
The players can react to any of these events. They can ignore them entirely. They can wander around the village attacking random cultist encounters. There's a general expectation that the group will meet the Protector of the village and offer to help (because, in the end, this is an adventure about heroes), but there's a lot of freedom for the players in DM in which encounters to use and how to approach each encounter.
What you're saying is: The DM presents an adventure hook to the players. The players can react to it or ignore it. Then the DM presents another adventure hook (of the DM's choice) to the players, and so on.
That is not a sandbox. That is a railroad. If the players ignore the dragon, nothing happens. If the players ignore the half-dragon, nothing happens. In other words: If they don't follow the plot, they don't get to play. Those missions are complete railroads and have no gameplay value. Additionally, both of those are actually
worse for the characters if they participate, since they have to use up resources on a task that doesn't matter!
Let's look at the other missions...
The Old Tunnel: Literally a straight line with monsters in the middle, and harder monsters at the end. The only sandboxy thing about this is the result: It creates another exit/entrance to the home base. There's even some mechanical support for it (every time they use it thenceforth, there's a chance that the enemies find it).
The Sally Port: The characters fight a group of monsters in a 10x20 room, then cast a specific spell, then fight another group of monsters. The potentially sandboxy thing about this is that if the PCs ignore it, more raiders can break through the broken gate. However, there's no support for that outcome, and it's not mentioned in the module at all (it assumes the PCs agree to the quest, and succeed), so it doesn't count.
Prisoners: This one makes no sense. Why do the characters have to bring the prisoner back to the keep? My players asked me this question, and I had no good answer. Either way, it's a non-adventure: go out, grab the first cultist you see, come back. How exciting.
Save the Mill: I almost lumped this one in with the dragon and half-dragon encounters, but there is one redeeming quality here: If the PCs realize it's a trap before going in, they can still get XP. However, it doesn't count because the text assumes the players go in anyway, which is stupid. The PCs can also get bonus XP for
succeeding on a passive perception check, which is even stupider.
Sanctuary: This one is the only significantly sandboxy mission. There's a clear goal, but many options on how to approach it. There are a few major problems with it, though:
- One approach is clearly better than all the others (and the text even points it out)
- There's no map or anything to help you if the PCs decide to take other approaches
- The outcome is scripted
There are a few good ideas in it, though:
- A dilemma that requires quick thinking from the players (essentially the same as the one in Tomb of Horrors, but much more forgiving in a variety of ways)
- The PCs get XP for each civilian they save, even they manage to avoid all the monsters (actually, the text says that's "in addition to the points for killing monsters," which is stupid, so it doesn't count)
That's one legitimately sandboxy idea in the whole first episode.
I have found memories of Wolfgang's Assassin Mountain and Secrets of the Lamp to this day.
