Beneath the Door provides a nice, concise list of all the “moving parts” for the adventure in the Moments section; establishing and maintaining a timetable of set events that happen during the course of your cosmic horror investigation—each of which will be revealed and appear differently to your players depending where they are in the evolving story they co-create with you—goes a long way toward creating a tone of mystery and discovery in this type of game, solidifying the genre and giving it a feel distinct from a dungeon crawl. NB: This is not railroading; the players can interact and interfere with the events on your list, but the mechanics of a “world in motion” that you bring to the table as a gamemaster create a desirable context for your players as they discover precious truths within the scenario.
Create ample opportunities for your investigators to “fail forward” during their investigation of events; sometimes the difference between “failure” and “success” in discovering and interpreting clues in a mystery game or other investigative scenario is only a matter of when in the timeline the revelation occurs.
Acquaint players with a Sanity mechanic and use it in your game. You can employ the included simple rules for loss from the adventure or crib a more nuanced set from another system or supplement, such as the Grit, Adrenaline, and Madness mechanics from The Waste Is Not Kind. I use one-heart Sanity rules that dovetail with a similar Luck mechanic in my homebrew cosmic horror adventures, in combination with Bouts of Acute Madness, as detailed in my short, easy-to-run cosmic horror hack for Master Edition, the Cthulhack…
The Cthulhack includes a reasonably broad generic list of trained and expert skills for investigators that make it easy to build a wide range of believable, effective, playable “normal human” characters for adventures in this genre.
If you decide you want to dive into cosmic horror with both feet running under ICRPG, I can recommend most heartily the genre hack Amid Infinity by @glocke, which is even more concise than my own, yet significantly more sophisticated in its approach…