But not sustainably forever - not without a mathematically (rather than just rhetorical) exponential rise in immigration or births, which is not being observed with respect to the 1940/50s as a baseline.
I don't get your problem. Even though I don't know any details, age adjustment means it adjusts for the aging population, it does not matter whether the birth rate or immigration increase.
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"All-cause age-standardized mortality rates for both sexes decreased by 29.0% between 1990 and 2015, falling from 584.1 deaths per 100 000 people in 1990 to 414.8 deaths per 100 000 people in 2015." https://healthsystemsfacts.org/national-health-systems/bismarck-model/japan/japans-health-system-outcomes/