I bought Myst 4 today, and I can't figure out how to get past the part when the girl drops me off at the platform (yes, the very beginning).

Welcome to the Myst 4 forums.

Since this is the wrong forums for hints or spoilers, I would suggest that you read "very carefully" the small booklet that is supposed to come with the game.

At the beginning I suggest you experiment the the "hand" cursor and see how it reacts to hot spots.(possible action required).

Check the small manual at page # 7, to see how the cursor can react at different spots.

If you need hints or non technical infos, start a "new topic" in this other forum...Myst IV Revelation - Spoiler Discussion...click here

(After leaving the shuttle and before going in, Yeesha did make a special move on something to open the door)