When a cruise ship heels a few degrees, what creates the first righting moment?

Answer: Offset buoyancy and weight

Offset buoyancy and weight ✓ — Right. When the ship heels, the underwater shape changes and the center of buoyancy shifts toward the low side. If the upward buoyant force no longer lines up with the downward weight force, the offset creates a righting moment. The surprise is that a ship can be stable even when its center of gravity is above the center of buoyancy; the metacenter, not just a heavy bottom, is the key.

Deep sailboat keel — Almost, but that is the sailboat intuition. A keel can lower the center of gravity, and narrow sailing yachts rely on that trick, but cruise ships get much of their initial stability from hull geometry. Their broad waterplane lets buoyancy move sideways when the ship heels, so the restoring leverage comes from shape as well as weight.

Ballast slides downhill — Not quite. Moving weight can affect stability, so it is a tempting mental model, especially once you know ships carry ballast water. But sloshing liquid is usually a free-surface penalty, not the first restoring mechanism. In a small heel, the hydrostatic shift of buoyancy relative to weight creates the righting torque.