Robin Hanson created a model of grabby aliens. In this model, we live before the arrival of an alien colonisation wave, because such a wave will prevent the appearance of the new civilizations. Thus, we could find ourselves only before the arrival of the aliens if any exists in our Universe.
However, at least some of the colonisators will preserve a fraction of habitable planets for different reasons: ethics, science, tourism, neglect. Let’s assume that it will be 0.01 of the total colonized volume. The numbers could vary, but it still looks like that in a densely packed universe the total volume of colonized space-time is significantly larger than the space-time for habitable planets before colonization arrival, and thus even a fraction of this volume could be larger than the volume of the virgin habitable space. This is because the colonized space will exist almost forever until the end of the universe.
Moreover, any small effort from the alien civilization to seed life (artificial panspermia) or to protect habitable planets from catastrophes like asteroid impacts will significantly increase the number of habitable planets inside the colonization zone. Hanson’s model also assumes that the probability of civilization appearance for any given planet is growing with time, so later regions will have a higher density of habitable planets, as more planets will reach this stage.
Given all this, our civilization has higher chances to appear after the colonization wave has passed us and thus aliens need to be somewhere nearby, but hidden, which is known as the Zoo Hypothesis. In other words, we live inside the sphere of influence of Kardashev 3 civilization which either helped our appearance via artificial panspermia etc or at least do not prevent our existence.
In this formulation, the idea starts to look like a variant of the simulation argument as here it is assumed that an advance civilization could create many non-advance civilizations.