Enough people to become majority in a few decades is not mass immigration? You really think this? These are projections for current immigration policy for several western countries.
From what you have said so far it seems you want a even more liberal policy, where these countries would be flooded with immigrants in maybe one decade, until they broke down
Population explosions in Africa are projected to lead to much more people wanting to move than now actually. In general, Africa is not a good place to live compared to the west
Already there are quite some signs of what's to come. Sharia courts for example are in place today in Britain(not above British law, but still operating as if being legal institutions)
Or you could look to South Africa, where white farmers now are being killed for being white, even a politician singing from stage stuff that strongly suggests killing of whites.