Let's think this through. Are best realistic speculations suggest the following parameters:

A) superluminal transits are unlikely
B) a colonizing generation/world ship would be massive, but not implausible
C) a colonizing generation/world ship may need to beging decelerating in advance of entering a solar system
D) Our random EM noise is not speculated to be indistinguishable from noise within a short distance (a couple lightyears or less)
E) We are not currently broadcasting a brighter radio signal that would serve to let someone there is a civilization already here or one that includes approach protocols.

Based on those assumptions, conflict is likely to result with first contact. It's most likely that if an alien species contacts us, it will be because they have decelerated into this system without realizing we were here and no longer have the capability to pass us by. Even if we manage to have peace initially, there will eventually be competition for resources.

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"What you think you thought you saw you did not see." Agent J, MiB - Manhatten Bureau