Installation:
Backup original MainMenuLoop.bk2 in root folder, where is installed your game, f.e. SteamLibrary/stemapps/common/Starfield/Data/video folder somewhere else.
Insert to Data/video one of the intros (bk2 file only) and overwrite.

Uninstall:
Overwrite with original file (back up).

To get rid of the original Starfield logo, use for example Cleanfield mod: https://www.nexusmods.com/starfield/mods/88

Credits:

Stargate movie Fanmade Alternative Intro Full HD: created by Mike Williamson and published by MISTER, Mike’s motion design and 3D company based in Sydney
Stargate SG-1 Intro Compilation: MGM, Amazon, for upload and video compilation YouTube user: Péter László
Stargate SG-1 Season 1-3 Full HD Intros: MGM, Amazon, for upload and upscale YouTube user: Classic TV Zone
Stargate SG-1 Seson 6 Special Intro HD: MGM, Amazon, for upload YouTube user: Ke-Karyu
Stargate SG-1 Season 8 Intro HD: MGM, Amazon, for upload YouTube user: 720ptv

No audio used. Original Starfield themes are used.

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Starage Kawoosh Mix

Credits:

MGM, Amazon, YouTube user: Peet Vas


Stargate Movie Wormhole Improved - Stargate Origins Wormhole Sequence (2018)

Credits:

MGM, Amazon, creator of this improved wormhole sequence: YouTube user Robert Wilde

No audio used. Original Starfiled themes are used. 

Creation of those video sources to bk2 by JackONeillSG1CZ