In response to your opponent, the active player, casting a creature, it is your desire to sacrifice three treasures in order to cast Cancel.
The activated ability of a Treasure token counts as a mana ability, per rule 605.
605.1a An activated ability is a mana ability if it meets all of the following criteria: it doesn’t have a target, it could add mana to a player’s mana pool when it resolves, and it’s not a loyalty ability. (See rule 606, “Loyalty Abilities.”)
Because it is a mana ability, the following applies, with emphasis added.
605.3a A player may activate an activated mana ability whenever he or she has priority, whenever he or she is casting a spell or activating an ability that requires a mana payment, or whenever a rule or effect asks for a mana payment, even if it’s in the middle of casting or resolving a spell or activating or resolving an ability.
605.3b An activated mana ability doesn’t go on the stack, so it can’t be targeted, countered, or otherwise responded to. Rather, it resolves immediately after it is activated. (See rule 405.6c.)
605.3c Once a player begins to activate a mana ability, that ability can’t be activated again until it has resolved.
You are trying to cast a spell, so you can use the mana Abilities of the treasure tokens to pay the mana cost of Cancel. Since they are mana abilities, they don't use the stack, so you don't need to mysteriously activate the abilities before your opponent casts the creatures.