I just now realized, after Izuna’s death Madara implanted his eyes to awaken his EMS. Then he had his battle with Hashirama, lost, made peace, they founded the village, he left, they fought again, Hashirama killed him, he revived himself with Izanagi and implanted the piece he bit out of Hashirama’s flesh that he swallowed and vomited into his wound, decades passed then he awakened the Rinnegan and summoned the Gedo Mazo and met Black Zetsu.
Madara awakened the Rinnegan in Izuna’s eyes, not the pair he was born with. Then he implanted them in Nagato. After Nagato died, Obito implanted the left eye in himself, being the fourth person to wield Izuna’s eye.