It was a whatthehell moment for me too. I started learning German a bit later than English (we had to learn 2 foreign languages at school). Pronunciation exercises brought the epiphany here, haha. Was strange at first but then we thought - hell, after all, these languages have much in common going back some centuries.
That's interesting, what's your native language? I found that the umlauts map pretty well to how a lot of people from GB pronounce their Us, As, and Os. If I had to transliterate the word "use" for example I'd write that as "jüs" in German.
God but I hated pronouncing the umlauts.