You can tap any untapped creature you control rather than pay a mana in the activation cost of Heirloom Epic’s ability, even one you haven’t controlled continuously since the beginning of your most recent turn.

If a creature you control has a mana ability with {T} in the cost, activating that ability to pay the activation cost of Heirloom Epic’s ability will result in the creature being tapped before you pay the ability’s costs. You won’t be able to tap it again rather than pay one of the mana in Heirloom Epic’s activation cost. Similarly, if you sacrifice a creature to activate a mana ability while activating Heirloom Epic’s ability, that creature won’t be on the battlefield when you pay the ability’s activation cost, so you won’t be able to tap that creature rather than pay one of the mana in the activation cost.

You can’t tap more creatures than the amount of mana in the cost of Heirloom Epic’s ability. Effects that increase or reduce the activation cost of Heirloom Epic’s ability apply before costs are paid and will increase or decrease the total number of creatures you can tap.