Immigration is largely irrelevant at the current rates of decline for many reasons. A simple one, and without any controversy, is plain old numerics. A shared fertility rate of 1 will trend towards you losing approximately 2.5% of your population per year, compounding. This is why Japan's current deterioration will be seen as the 'good ole days' in the future - they're currently "only" losing about 0.5% per year. So after 80 years, a single human lifetime, your population declines by 87%.

There simply are not enough people to replace this sort of decline, even if you just grab anybody regardless of skills, education, or even the ability to speak your language - which is not exactly a great recipe for a healthy country. Like if 60% of the world, by population, is losing 80% of their population over that timeframe, that'd be a global population decline of 48% with only 40% of people in the rest of the world. You'd need all of them and then a good chunk of their babies too, and that's for less than one human lifetime of change.

I'd say immigration is just kicking the can, but it scarcely even counts as that given how little of an effect it can have even at theoretically absurd levels.