How do you mean "a list of effects"? as in something happen and right after that something else started happening or, something happens without expectation?
Like for example... "As soon as I entered the room, the lights went on" or "Unexpectedly rain started to fall".
If so I'd say either "Suddenly" or "All of the sudden"
So: "As soon as I entered the room, suddenly the lights went on"
"Suddenly/All of the sudden rain started to fall"
Soon
has pretty much the same meaning but kinda... delayed, suddenly is for instant, soon, may be prolonged even to few weeks (depending on how urgent something is, it's still soon). Also suddenly usually refers to something surprising happening.
Consequently works if something happens as a result of some first action.
"I studied a lot and consequently I got good score on a test"
As a matter of fact
doesn't really work with these imo...
because you're explaining something, usually contradicting the expectation of someone else, or their statement for example...
"A: You weren't there, so you don't know how it happened.
B: As a matter of fact, I stood right next to you, you just didn't notice me."
or
"A: I hate <something> same as you hate dogs.
B: As a matter of fact, I love dogs."
