The places where the immigrants are coming from are getting richer and their birth rates are dropping so there won't be enough immigrants to grow developed nations' populations.
People will just have to learn to run countries with a stable population.
Developed countries are all dropping below replacement fertility rate, sustained only by immigration and the higher fertility rate associated with recent immigrants.
I haven't seen any evidence for a stable point of population - it looks like it will grow, until it begins to decline in the not-too-distant future. Then does it ever stop declining?
Does it stop declining at a point we can sustain a technological society, much less technological progress?
That's my vote for resolution of the Fermi paradox.
I blame young women, who don't want to get married and don't want to have children. Sigh. It may be that western culture will collapse on its own when it reaches a certain point.
People will just have to learn to run countries with a stable population.