If you want to deal with the issue at more 'leisure', engineer something behind your (currently closed) entrance, or behind another potential entry that you haven't opened yet, a long-ish winding route with drawbridges at either end for isolation purposes. Then withdraw your workforce further in, open your entrance (or breach this new entryway, and impress upon that worker the need to start doing something else well inside the fortress
immediately) and if the Cyclops is bothered at all he'll wander into this prepared area, you can pull the lever to make the isolating drawbridges to raise/retract and then you can get on with life.
I suggest something like
v v
#################
=.=...=...=...=.=
#.#.#.#.#.#.#.#.#
#.#.#.#.#.#.#.#.#
#.#.#.#.#.#.#.#.#
#.#.#.#.#.#.#.#.#
#.#.#.#.#.#.#.#.#
#.#.#.#.#.#.#.#.#
#.#.#.#.#.#.#.#.#
#.#.#.#.#.#.#.#.#
#.#.#.#.#.#.#.#.#
#.#.#.#.#.#.#.#.#
#.#.#.#.#.#.#.#.#
#.#.#.#.#.#.#.#.#
#.#.#.#.#.#.#.#.#
#...#...#...#...#
#################
Scale according to your opportunity, probably doesn't need to be anything like that size, whether you dig it out or construct it above-ground with walls.
#: walls; .: floors; =: retracting, with the two bridges pointed to with the 'v' being the isolation ones, and the others (if needed, else make those spots just wall) being the 'quick escape' route of any worker that's needed to quickly travel through, set to a second lever that's pulled as soon as said worker has dashed through the short-cut. (Or all but done so, if you're cutting it fine...
)
Below all the bridges, make sure there are no ramps, of course.
Above this level set Fortifications over the 'path' and then if/when you get archers up there they can still fire down on whatever is trapped (also works for goblin attack squads and other enemies, and for some enemies a tethered sacrificial creature or a building that can be toppled might be required), without risk of falling down, themselves.
It's also possible that you might use such a device to entice enemies in one direction so that the likes of your recent migrants can wander along into another entrance, but that heavily depends of relative positions of each party and the fortress entrances. Plus not having to construct it
very very quickly given you haven't done so already.