For example: Is it "Meinem Vater schmeckt Pizza sehr" or "Mein Vater schmeckt Pizza sehr"?
Any part of speech can be put at the start of a sentence (although in the case of verbs, that makes the sentence a question. A verb always comes second in a statement.)
Ich habe das Buch meinem Vater gegeben. I gave the book to my father.
Meinem Vater habe ich das Buch gegeben. To my father I gave the book.
Das Buch habe ich meinem Vater gegeben. The book I gave to my father.
Später habe ich das Buch meinem Vater gegeben. Later I gave the book to my father.
Habe ich das Buch meinem Vater gegeben? Did I give the book to my father?
The "start" position is used for emphasis, and the declensions or "cases" of the various nouns is used to determine their function (nominative for subject, accusative for direct object, dative for indirect object). Verbs and adverbs are self explanatory.
Yes, it can. Your example is a correct german sentence. Why would you think, it was wrong?