This article contains speculation, information which has not been confirmed by a reliable source. The game is still in development, and all information is subject to change.
Another dynamic mission seen in the gameplay trailer is the "Defend Dredge" mission. The short descriptive text displayed reads "Stop the Chosen invasion", and the longer descriptive text reads "Defend Dredge from the Chosen invasion." Followed by prompts to left-click the mouse to accept the mission, and right-click to decline. Presumably, declining the mission bars you from interacting with the invaders in that mission, but this is purely speculation.
Also, during the Defend Dredge mission, another dynamic mission pops up to "Destroy the Titan". Mission alerts seem to remain on the left-hand side of the screen until you choose to accept or decline them.
The only active post-intro quests are the daily resources from Ratched and the SIN-uplinks.