What's a "sustainable" fertility rate to you? Given that the current human biomass is completely unprecedented in all of history and is only made possible by artificial energy inputs (fossil fuels and ammonia/fertilizer), I posit that the only sustainable fertility rate is well below 2.0
When discussing fertility rates "sustainable" usually means "ratio of births to deaths in order to have a stable population". In developed economies that's around 2.1 children per woman. Anything under that and the population declines without immigration.