I don't know if I'd call it a slow start, but, before the corpse turns up/the monster jumps out of the shadows, I like to at least have some idea of what sort of Normal this event is overturning. Who is the main character? What do they want, what is their life like? If I don't know who/what is being thrown into danger or chaos, it's harder to care whether they make it out the other side.
I do think there's a balance, though, where you want to at least hint at what is coming while you are doing your introduction/build-up. I'll risk using my own story as an example, even though I'm honestly not sure yet that I've pulled it off well enough. It takes a bit of time (twelve pages or so) for the MC to stumble across her colleague's body. But before that, she receives a phone message from him, in which he sounds not at all like his normal self. So there is already the suspicion that something isn't right. This suspicion colours the way we are introduced to her world - we see this extraterrestrial colony filtered through her worry that something could be wrong with it.
So my opinion (largely echoing others above) would be, take a little time if you need it to introduce your characters and world, but weave in hints or background murmurs of wrongness that remind us we are walking with the MC towards something horrible.