You can trigger the cutscene from a trigger activation field like you would via an INIT field.
So if your cutscene script is blah.sqs
this exec "blah.sqs"
in trigger activation.
If the cutscene is in your INIT.sqs script, rename the file to something, like cutscene01.sqs, and call this when you need it.
Remeber that things can be moved about, shot and blowen up, so if your cutscene uses a soldier, say, it is possible the player might have shot him, or parked a truck in the way etc..
- Ben