Learn Turkish: Güneş doğdu.

This is because of 4-way vowel harmony! The witnessed past tense suffix changes to match the last vowel of the verb root. The verb root here is doğ-. Since its vowel is o, the suffix becomes -du. (The rule is: if the last vowel is o or u, the suffix uses u).

Is there a suffix at the end of doğdu to show that it means "it" (the sun)?

No extra suffix is needed! In the Turkish past tense, the 3rd person singular ("he", "she", or "it") is indicated by the absence of a personal ending. You just use the verb root (doğ) plus the past tense suffix (-du). The lack of any ending after -du tells you the subject is a 3rd person.

Wait, doesn't doğmak mean "to be born"?

Yes, it does! In Turkish, the sun, moon, and stars are poetically thought of as being "born" when they appear in the sky. So to say "the sun rose", you literally say "the sun was born" (Güneş doğdu).

Why isn't there a word or suffix for "the" attached to Güneş?

Turkish doesn't have a definite article like "the". Furthermore, when a noun is the subject of a sentence (the one doing the action), it stays in its plain, dictionary form. So Güneş simply translates to "the sun" here based on the context.