This mission is explained with a high amount of more detail in the video, which I highly recommend you watch it:
To speed run this mission, start the timer after skipping the beginning cutscenes and the load fades out. Sign in and get dressed, after this, go into Samuels room, Walk in far enough that Samuels will begin talking and then walk out and go into Taylor's room. Do the same process, and than go back to Samuels once you walk away from Taylor. Let Samuels finish talking and when Ripley starts to say "Haven't seen her..." you can walk out. Then go back to Taylor and get the loot in that rim. Verlaine will call you guys up, and you will retrieve the Briefing Files. Skip the next cutscene and split to Mission 2.
Written by: WickednessForThriven
Video by: PyschoHynotic