Questions & Answers about Gestern frühstückten wir schnell, weil der Wettbewerb früh anfing.
Because the sentence is in the Präteritum (simple past), which is often used in written narratives or formal registers. Frühstückten is the 1 st person plural Präteritum form of frühstücken. In spoken or informal German, you’d typically use the Perfekt:
Gestern haben wir schnell gefrühstückt, …
Gestern is a temporal adverbial placed in the first position to set the time frame. German follows the “Time-Manner-Place” (TMP) rule for adverbials, and when an adverbial comes first, the finite verb occupies the second slot, causing subject-verb inversion:
[Adverbial] + Verb + Subject + …
so you get Gestern frühstückten wir …