@Dragonrider's Fury, would it be okay if you could work on the script instead of me? The basic idea I have for the beginning of the game is this.
Before the events of the game, your character was captured by the dragon trappers for some reason (maybe they threatened to report the trappers to the local chieftain for illegal poaching on the land), and they were taken onto the ship. Fortunately, it's the same one that Hiccup and the other riders (
) have planned an attack on (since I assume they started rescuing dragons straight after HTTYD 2), and they begin their raid. Hiccup notices that the player character has been captured, and he tries to free them. But while he was distracted with trying to rescue you, he didn't see that the trappers have launched a surprise attack on the other riders, capturing them and their dragons. Still not realising what's happening, Hiccup finally manages to free your character, gets on Toothless, and tells you to climb on behind him. Toothless takes off, but as part of the trappers' surprise attack, he is hit by a net and you are all knocked out.
The game starts with your character waking up in a cell with Hiccup, who figures out a plan for escaping and finding Toothless. When he is rescued, Hiccup finds the other riders and their dragons. Toothless frees them from their cells with a plasma blast, and Hiccup gets on Toothless again, with your character climbing on behind him. The other riders mount their dragons, and they all fly back to Berk.
Once your character is on Berk, Hiccup asks to speak with you. He says, 'Thanks to you, my friends have their dragons back, but you don't have one. I think we should do something about that.' He hands you a map of the island and tells you to go wherever you want to find your dragon. Hiccup also gives you a smaller version of the Book of Dragons, containing everything he knows about all the dragons he's seen, which you can keep in your pocket during your journey, and he says that it will help you choose which dragon you want. Then you're free to explore — look around the village, see if people need any help, and when you're ready, you can go into the wilderness of Berk to choose your dragon. After you've done that, you see Hiccup flying to your location on Toothless. He teaches you how to tame your new dragon, and he also shows you how to fly him/her. Once you've finished that, the beginning of the game is completed, and you can leave Berk (which unlocks the main quest 'Beyond Berk'). You are free to explore the entire Barbaric Archipelago!