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.)
§ 506.3.d Tournament Rules PDF (officieel)
§ 506 Triggered Abilities
§ 506.3 The accountable player must acknowledge their triggers by the time they would have an observable impact on the game. If they do not, they are forgotten.