There is disagreement about when the peak will be reached. As your link shows, the UN puts it in 2086. The Global Burden of Disease Study published an article in the Lancet putting in 2064. The UN projection is solely based on current demographic trends and assumptions regarding life expectancy are quite optimistic. I have seen at least one study put the peak in the 40s while arguing that the rate of decrease in the total fertility rate is underestimated which while not likely is not impossible - historically predictions of variation in the TFR have not been very accurate.

Generally, the impact of potential feed back loops including climate change are understudied. There is a convincing argument to be made than worsening conditions could lead to the peak happening sooner.

At the end of the day, models remain models. They are not exact forecast. It's important to keep in mind when people argue we are doomed based on them.