An obvious alternative would be adopting policies to raise the domestic birthrate to the population replacement rate, e.g. increasing the child tax credit, and various policies to disconnect housing costs from school quality so that prospective parents don't change course when they see how much more it costs to buy a house in a good school district.
Automation hits some industries harder than others. It's barely affected restaurant workers, for example, but has decimated mining labor.
Another recent example is processing meat. The US has a shortage of labor, but robots can't do the work and Americans refuse to.
Further reading: https://en.m.wikipedia.org/wiki/Alabama_HB_56#Impact
https://www.japantimes.co.jp/opinion/2019/06/26/commentary/j...
https://topics.amcham.com.tw/2018/11/taiwan-embraces-southea...
https://www.forbes.com/sites/ralphjennings/2018/03/19/taiwan...
If birth rates are low, how does your economy function with many older workers who can't/won't do labor like construction?
Why is Japan opening itself up for immigration specifically to fill jobs? What other solution should they have chosen?
Do you have a concrete policy proposal for a country like today's Japan?
As far as the claim that capitalism doesn't require infinite growth: that doesn't seem mathematically possible, ans it's certainly an unorthodox claim. I'd say that puts the burden on you to provide evidence (or, at the very least, explain).
the basics of econ, growth isn't even mentioned when it comes to capitalism.