Not sure it's the same problem you have as the usual mad carriage some have experienced here.
Just in case it would help, here are some tips :
The Helgen sequence is heavily scripted, so as your game engine is quite busy, it could simply be the fact you have too much scripts running at the same time, at the beginning of the game, creating a latency that prevents the scripts in queue from working in due time.
/// 1 - You may use A workaround here. This is a simple mesh replacer that will prevent the carriage from going mad.
/// 2 - Untick from launcher / mod manager all your heavy mods BEFORE starting a new game, especially those using scripting. Keep those you use to create your character. Make a save and once the Helgen sequence is done and you're out, reactivate/install your mods.
/// 3 - You can instal LAL to avoid the vanilla start.
/// 4 - If unfortunately above things don't work, there are other leads in this topic...
- Make sure you have vsync turned on.
- Make sure your framerate isn't going above 60 - use a fps limiter or the ENB limiter included feature or using your graphic card utility if you experience problems with the ENB limiter.
/// 5 - Some of the skyrim.ini [papyrus] settings can have very bad effects on the way the game handle scripts, Read here why.