That's false, though a common myth. Norway was already a fairly wealthy country before the discovery of oil. Norway was always fairly strong in trade, and after it got hydro-power there were already industry giants like Norsk Hydro, and there was plenty of natural resources other than oil.
Norway is surprisingly diversified for an oil nation. Just look at a breakdown of exports of Norway vs other countries where oil/gas dominate.
Qatar: https://commons.wikimedia.org/wiki/File:Qatar_Product_Export...
Norway: https://commons.wikimedia.org/wiki/File:Norway_Product_Expor...
While oil/gas is a huge share of exports, since there's hundreds of various industries that's already well-established, it's not gonna be too hard for those industries to absorb the capital and labor which is freed up when the oil/gas industry winds down.
My experience with an industry outside of oil and gas in Norway, is that the industry has a growth which has been severely hampered by lack of capital and lack of labor. We could easily double in size over the span of a decade, if the capital and labor pool doubled.
It is misconception that Norway was poor before it found oil. Statistically Norway did as well as or better than – based on GNP per capita – most other European countries from 1830-1938; similar to Germany, https://en.wikipedia.org/wiki/List_of_regions_by_past_GDP_(P...