The income from the wealth fund doesn't need to replace oil income forever, it should be used to invest in growing other parts of their economy. For example, Equinor is getting into offshore wind and carbon sequestration both of which use similar competencies to oil production.

Anyway, they are still extracting oil and probably will continue to do so for a couple decades. That gives them time to grow their wealth fund and gradually transition their economy. They are at a huge advantage compared to other oil exporters.