1: Download and install "The RAD Video Tools" from the Bink Video website.[www.radgametools.com] (Yes, it's trustworthy. You might recognize their logo from the end of the intro we're going to be editing.)
2: Run "RAD Video Tools" and navigate to where Doom's .bik files are. (C:\Program Files (x86)\Steam\steamapps\common\DOOM\base\video by default.)
3: Single click on "boot_sequence.bik" to select it.
4: Click the "Bink it!" button at the bottom left corner of the window.
5: In the "Input video settings:" section, under "Frame range:", set "Start:" to 0 and "End:" to 1. This cuts the video down to only those frames, making the video as short as possible.
6: Click the "Bink" button at the right of the window.
7: Click "Done" on the box that pops up when the compression is done.
8: Navigate to where the .bik files are in File Explorer.
9: Delete "boot_sequence.bik" if you've not done that already.
10: Rename "New_boot_sequence.bik" (the file created in the above steps) to "boot_sequence.bik".
11: Launch Doom, there should be a black screen for a few seconds and then it will start loading.

This works because the game plays the "boot_sequence.bik" to completion no matter how long or short it is.