I believe that a random event like the alien invasion, during any age of play, is right that it is present. It must be a fairly rare event, but it must be there.
The probabilities of invasion should increase if we find ourselves in an industrial phase where technology starts sending radio waves in space (even involuntarily because of the first radio communications).
The chances of invasion should increase even more if, after the discovery of the radio waves, messages are sent in space or to certain stars in the hope of finding an answer. (For example our SETI)
In this case, one could also receive a response message from another civilization that is still in the industrial age / the first space was still impossible for space travel.
Taking into account the Stellaris game, the invasions by a stellar civilization towards a primitive civilization (Stellaris considers primitive any civilization between the stone age up to the first space age) are always successful for the invader. The only way to lose some battles and those to send on the planet a not large number of units that will be defeated with great difficulty by primitive civilization (civilizations that have however at least reached the era of the atom, ie that before the first space age ).
However, primitive civilizations can not do anything against orbital bombing.
Trying to be a little more meticulous than Stellaris, I believe that an industrially advanced civilization / early stage phase may have some chance with a young space civilization.
A young space civilization may have not yet discovered the technology of space ship shields, making them attackable by nuclear attacks.
A young space civilization may have been automating their industries with robots, but perhaps they have not yet managed to create robots that are sufficiently efficient to deal with military tactics elaborated by sentient beings, thus preferring to send soldiers of their race to the planet’s soil. .
I think the only scenario of confrontation almost on a parity is this (despite the young civilization space remains in clear advantage at 80/20 - 75/25).
But if instead the primitive civilization was found in any other phase, or if the young civilization of space was more evolved, there would be no possibility of victory for the defenders if not more or less long periods of vain resistance.
What do you think?
P.s. sorry for my bad English