Non-Omicron variants like Delta are only extinct in the sense that they are no longer widespread in the general population. Even so, they continue to mutate in chronically infected people for years, resulting in variants that make even Omicron look "pedestrian." https://www.nature.com/articles/d41586-022-02996-y

Here are three Delta variants detected this January, one of which got up to over 90 mutations: https://twitter.com/LongDesertTrain/status/1624464486596849670

This might be how Omicron started and how the next big variant emerges.