Cast Orcish Bowmasters by paying its mana cost; it enters with a vigilance counter due to Tayam.
When Orcish Bowmasters enters, it triggers, dealing 1 damage to any target and 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 Orcish Bowmasters and the creature token, adding {C}{C}{C}{C}.
Resolve Tayam's ability, milling three and returning Orcish Bowmasters 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 damage

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

Orcish Bowmasters

Activate Wall of Roots by putting two -0/-1 counters on it (due to Winding Constrictor), adding {G}.
Activate Tayam by paying {3} and removing three counters from creatures you control.
In response to Tayam's ability, activate Ashnod's Altar by sacrificing Wall of Roots, adding {C}{C}.
Resolve Tayam's ability, milling yourself three cards and returning Wall of Roots from your graveyard to the battlefield with two vigilance counters on it due to Tayam and Winding Constrictor.
Repeat.

Winding Constrictor

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