Futurists forecast the mid-term future (
+centuries) of earth civilization to be something like the
Expanse, with societies & economies spreading throughout the Solar system (Kardashev-I). Gradually (
+millennia), dispersed settlements & industrial sites will accumulate until Sol is surrounded by a Dyson Swarm (Kardashev-II):
With essentially 100% of Sol's power output harvested, the only room for continued growth would be in other star systems. The Dyson Swarm, essentially a space-worthy fleet of long-term sustainable mobile space habitats, would reduplicate itself... and the copies would migrate
en masse to some suitable second star system.
If so, actual interstellar space-travel is not undertaken by lone explorer craft, but by massed "Zentraedi fleets" of specialized Dyson Swarm vessels ("Nina, Pinta, Santa Maria, Magellan's fleet, Vespucci's fleet, and everyone else's too"):
Such mobile Dyson Swarm super-armadas would arrive in the target destination system like "locusts descending on all Egypt at once" (and by "locust" we mean "Locust CV" aerodyne class worldship larger than an aircraft carrier), appropriately positioning pre-specialized units designed for processing rocky terrestrial inner system worlds, others for siphoning hydrogen fuel from gas giants in mid system, still others for electrolyzing icy outer system objects, all essentially simultaneously throughout the star system.
Plausibly, there would initially be some "rest, refit, repair" phase immediately after the enormous interstellar undertaking. But with surprising swiftness, the Swarm would quickly proceed to processing system material, and constructing the next wave of colony craft.
If so, once a civilization reaches K-II level, they possess the equivalent of mobile Dyson Swarms, which can completely enshroud target destination star systems immediately upon arrival. Such that Visited star systems would immediately "go dark & drop off the radar" without any of the gradual dimming (theoretically) detectable in the original home star system, on the progression from K-I to K-II, ages & eons before.
If you don't detect an emerging K-I on its way to K-II, in its original needle-in-a-cosmic-hay-stack system, thereafter your only evidence would be galactic lights "shutting down like an EMP knocked out the power grid".
Offer that inter-
galactic colonization would involve
numerous such Dyson Swarms, which would plausibly make "galaxy fall" somewhere in the outer reaches and start "chewing their way inwards"