You have to use the search feature to look for tweets and then look at the parent tweet ID. This is what bots like threadreaderapp, etc do. You can construct it from the bottom up if you know the ID of the last tweet in the thread of responses too, but you wouldn't know that a priori unless the user gives it to your software somehow.

But... that's not a tree -- there's still no way to discover all leaves. That's just a thread/singly linked list.

Yes, I forgot to mention that. You need to know the IDs of all the leaf nodes of the thread or else you can only partially reconstruct it.

so the api is literally backwards

Step 0: build a tree including all tweets,

...

;)

Possibly using the HTML API.

The final frontier