The Arena's Greatest

190.6.b. While a Battlefield is Uncontrolled , its Abilities are also Uncontrolled unless that ability indicates a player controls it. If there is no such indication, the Turn Player takes responsibility for adding them to the Chain if applicable, makes all choices required by them unless otherwise specified, and is treated as their Controller if any game rule or effect requires one. Example: The Arena's Greatest is a battlefield that reads "At the start of each player's first Beginning Phase, that player gains 1 point." This ability will usually trigger while the battlefield has no controller. If it does, the Turn Player goes through the steps of adding the ability to the chain and receives priority after doing so, exactly as if they controlled the ability.

506.3.d. For triggers that occur "At the start of each player's first Beginning Phase", the accountable player has the full duration of the turn in which the trigger occurs to acknowledge the trigger before it's considered forgotten, regardless of its observable impact. (Example cards: Obelisk of Power and The Arena's Greatest.)