Immigration won't work because of the scale of the problem. It's another concept that was probably based on the flawed UN projections this article talks about. Take a fertility rate of 1 for an easy math example. Most countries aren't this low yet, but it's fair to say that this is the trendline. Once we reach the 'equilibrium point', where your entire population has this fertility rate or, in other words, when the last high fertility rate generation dies off, this would result in your population declining by 50% every ~20 years. And this is an exponential system - you lose 50%, and then 50% of what remains indefinitely every 20 years. And this continues until you go extinct, or start having children again.

So consider what this would look do to a nation's population over just a single human lifetime - 80 years. China would go from 1.4 billion -> 0.7 -> 0.35 -> 0.175 -> 0.0875 billion. That's China going from 1.4 billion to 87.5 million, the size of Germany, in a single human lifetime. The US would go from 330 million -> 165 -> 82.5 -> 41.25 -> 20.625, the size of Chile, over the same time frame. And this process doesn't stop, it just keeps going.

You would need to essentially replace your entire population with immigrants. And of course you don't just need massive amounts of warm bodies. You need skilled, educated, sex ratio balanced (which means more women than men due to differing mortality rates - men get themselves killed far more frequently), people who are capable of speaking at least reasonable English. There simply aren't enough people in the world to fulfill this in practical terms. And this is just speaking from a technical point of view in terms of scale of the problem. I'm intentionally avoiding the more controversial social, cultural, and other aspects involved in such a process. It's all just a nonsolution. Immigration can briefly help patch a small-scale problem, but at scale it's like trying to keep a sinking boat afloat with a bucket.