Battle With Ace
When she fought Ace, she stalemated him.
Ace declared that she was too strong to not be the Captain.
Note that Ace is saying this about an Emperor’s crew.
This same sentiment has also been expressed of Zoro, and Zoro revealed himself to be a Conqueror:
Yamato has disowned Kaido has a Father.
She desires to face him in combat.
She destroyed the dragon statue that symbolised his power.
This might signify her rejection of his authority and dominance over her life.
Yamato has an incredibly good case to be a Conqueror — about the strongest of those not yet confirmed to be Conqueror’s we’ve seen among the new generation — and I would be surprised if she’s not.
She sort of needs Conqueror’s Haki (even if she has to learn/awaken it mid combat) to be able to put up a real fight vs Kaido.
Thematically, it would also fit for her to get a Conqueror’s clash with him as she rejects his influence over her life and forges her own path forward.
Her heritage is the strongest we’ve seen of any top tier’s children. She inherited her father’s abnormal body, his weapon and even his fighting style. Kaido himself also holds very high ambitions for her.