Is it possible to skip Skyrim's new game introduction cinematic?

The game automatically saves the game just before the Imperials start reading off names.

Once you've played through the intro once (and assuming you haven't turned off Auto-Save) you can always load that game: It should list your name as "Prisoner", your Race as "Nord" and your level as "1". (And is likely save 001).

A savegame right after the introduction can be found at the Skyrim Nexus

If playing on the PC or Xbox One, installing the Alternate Start - Live Another Life (PC) / (Xbox One) mod will allow you to skip the game introduction cinematic at Helgen. It will offer a choice of which location you want to start in (you can start the game in Dawnstar, for example).

Live Another Life provides an alternative means to start the game for those who do not wish to go through the lengthy intro sequence at Helgen. You will be given the opportunity to choose your race and then choose a new life for your character to lead. A wide variety of choices will be available...