Whilst there isn't any specific in-universe answer to this, I thought I'd provide a mixing of "real world" and ST universe that could provide an answer.
Within the human genome, there is a limit to the number of variations of our genes. Given that only a portion of those genes provide for physical characteristics, the odds on duplication are even higher. You can see this in day to day life with celebrity lookalikes (although admittedly some of the lookalikes are tenuous at best).
Given this limitation, as the number of members of the species increase (e.g. due to planetary migration), the likelihood of people who look alike will increase.
This BBC article discusses the likelihood of having doppelgangers around the world.
So that provides a possible explanation for intra-species lookalikes. But what about inter-species lookalikes?
For that, we need to turn to the ST:TNG episode: The Chase with the above in mind. In this episode, factions from several species attempt to chase down a weapon hidden within the genetic code of species from all over the quadrant.
In the end
They discover that the code produces a hologram of a genetic progenitor. Whose race sought to create new races in their image.
The script for this episode can be found here. But the relevant section is quoted below:
Our scientists seeded the primordial oceans of many worlds, where life was in its infancy. These seed codes directed your evolution toward a physical form resembling ours -- this body you see before you.
So, since all the races share this in common, it would not be a large stretch to extend the likelihood of doppelgangers to all humanoid species, rather than just humans.
As a fun-fact, its worth mentioning that the hologram in The Chase is played by Salome Jens. If she looks familiar, that's because she also plays the main Founder in ST:DS9