Cast Vizier of the Scorpion by paying its mana cost; it enters with a vigilance counter due to Tayam.
When Vizier of the Scorpion enters, it triggers, creating a 0/0 creature token with a +1/+1 counter on it as well as a vigilance counter due to Tayam.
Declare that you are activating Tayam's ability, so state-based actions will not be checked until the ability is activated.
While paying that ability's cost, activate the creature token using the Wall of Roots mana ability from Agatha's Soul Cauldron by putting a -0/-1 counter on it, adding {G}.
Complete the activation by paying {3} and removing a vigilance counter from each of the two creatures and a -0/-1 counter from the Army token.
Holding priority, activate Ashnod's Altar twice by sacrificing Vizier of the Scorpion and the creature token, adding {C}{C}{C}{C}.
Resolve Tayam's ability, milling three and returning Vizier of the Scorpion from your graveyard to the battlefield with a vigilance counter on it.
Repeat from step 2.

Infinite creature ETB

Infinite creature LTB

Infinite creature sacrifice triggers

Infinite death triggers

Infinite self-mill

Infinite colorless mana

Infinite green mana

Wall of Roots

Agatha's Soul Cauldron

Tayam, Luminous Enigma

Ashnod's Altar

Vizier of the Scorpion

Cast Vizier of the Scorpion by paying its mana cost; it enters with a vigilance counter due to Tayam.
When Vizier of the Scorpion enters, it triggers, creating a 0/0 creature token with a +1/+1 counter on it as well as a vigilance counter due to Tayam.
Declare that you are activating Tayam's ability, so state-based actions will not be checked until the ability is activated.
While paying that ability's cost, activate the creature token using the Wall of Roots mana ability from Agatha's Soul Cauldron by putting a -0/-1 counter on it, adding {G}.
Complete the activation by paying {3} and removing a vigilance counter from each of the two creatures and a -0/-1 counter from the Army token.
Holding priority, activate Phyrexian Altar twice by sacrificing Vizier of the Scorpion and the creature token, adding two mana.
Resolve Tayam's ability, milling three and returning Vizier of the Scorpion from your graveyard to the battlefield with a vigilance counter on it.
Repeat from step 2.

Phyrexian Altar

Cast Vizier of the Scorpion by paying its mana cost; it enters with a vigilance counter due to Tayam.
When Vizier of the Scorpion enters, it triggers, creating a 0/0 creature token with a +1/+1 counter on it as well as a vigilance counter due to Tayam.
Declare that you are activating Tayam's ability, so state-based actions will not be checked until the ability is activated.
While paying that ability's cost, activate the creature token using the Wall of Roots mana ability from Agatha's Soul Cauldron by putting a -0/-1 counter on it, adding {G}.
Complete the activation by paying {3} and removing a vigilance counter from each of the two creatures and a -0/-1 counter from the Army token.
Holding priority, activate Thermopod twice by sacrificing Vizier of the Scorpion and the creature token, adding two mana.
Resolve Tayam's ability, milling three and returning Vizier of the Scorpion from your graveyard to the battlefield with a vigilance counter on it.
Repeat from step 2.

Thermopod

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