The part about no support isn't really true, at least in the Netherlands. There has been an endless stream of government programs, and billions upon billions of euros invested, which unfortunately had only a small effect. So I have little hope that the current immigration will go significantly better. I don't know if there's a magic trick, but if there is we certainly haven't yet figured out how to perform it. Even in cases that seem very successful the results aren't as good as you'd hope. The mayor of the second biggest city in the Netherlands is Moroccan, and he has said that he will not allow his daughter to marry a native dutch man. The theory that it's all about not enough support doesn't explain the fact that there are lots of successful groups of immigrants, like the Chinese. They have high employment rates and low crime rates. Therefore I don't really like the talk about the failure of multiculturalism.
The studies show that second generation of migrant (from Asia and Africa) women don't have that many more children than Europe's natives (contrary to what the populist anti-migrant propaganda is pushing) - in most countries the difference was on the order of 0.3 - 0.5 children per woman if I remember correctly.
Poland tries to address the fertility issue in a different way - we're letting in lots of Ukrainian migrants (currently there's 500k of them working legally in Poland, with probably another 500k working illegally). They are a much better match, as their language, culture, values and even parts of history are close to ours.
However, if you look at the demographics in europe we either need to get better at integrating people from other countries and cultures or we need to get more babies - because there are no other options (barring any sudden development on the AI/Android front). I doubt forcing women to get more children is a viable option. Banning all abortions as Poland tries to is not going to help. This problem may not be as obvious in Poland as it's in Germany, but they're already suffering from brain drain - the young and educated move away from eastern Poland. Things will only get worse - so it's not a question of want or not want. We - as in all of us europeans - will have to deal with immigrants one way or another. And we can do it as unprepared as germany was in the 60ies/70ies or we can learn from that debacle and try to improve on that.