Madrugada refers to the very early hours of the morning, typically from midnight to dawn. It's a more specific and evocative term than just "morning."
In the song, the phrase "gato de madrugada" (cat of dawn/early morning) paints a vivid picture of loneliness and aimlessness. The singer feels abandoned, wandering like a stray cat in the quiet, desolate hours before sunrise, searching for a way out of his emotional predicament. This word captures the melancholic and solitary mood of the song.
Joss Favela's "Gato De Madrugada" is a heartfelt song about the aftermath of a breakup, told from the perspective of someone grappling with loneliness and regret. He's looking back, wondering how he ended up "parado hoy aquí" [standing here today], realizing it's the sum of past decisions. He misses the intimacy they once shared, remembering a time when his partner's parents' couch was "una suite para los dos" [a suite for the two of us], a place for laughter, dreams, and learning to love.
The singer feels abandoned, left "solo aquí, sin nada" [alone here, with nothing], comparing himself to a "gato de madrugada" [cat at dawn] wandering the rooftops of life without finding a way out. Even though he might have "todo" [everything] materially, he's missing her unique kisses. He looks up at the sky, asking, "si no me hace falta nada, ¿Por qué me haces falta tú?" [if I don't lack anything, why do I lack you?] and wonders if she ever misses him too. It's a really relatable feeling of emptiness despite having everything else.