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No you didn't miss the Game of Thrones theme song from the first episode of A Knight of the Seven Kingdoms

With Game of Thrones and House of the Dragon using the same opening credit music, you likely expected it on A Knight of the Seven Kingdoms. No, you didn't just happen to miss it. It's not there.
Gizmodo

You Will Hear the ‘Game of Thrones’ Theme in ‘A Knight of the Seven Kingdoms’ (But Not in the Way You’d Expect)

Showrunner Ira Parker explains how the iconic music finds its way into HBO's latest journey to George R.R. Martin's Westeros. Reading time 3 minutes Fans of Game of Thrones had a sort of chuckle mixed ...