Can gigantes be special summoned from your deck?

No, it can only be special summoned initially from your hand by removing one earth monster from play.

Effects that special summon monsters from deck, cannot special summon a monster which is 'special summon only' because these monsters have to follow their own summon method. So you cannot special summon Relinquished using Mystic Tomato, it has to be Ritual Summoned or otherwise summoned by a card that says it can summon Ritual Monsters.

Likewise, Gigantes can't be special summoned from deck by an external effect, and of course can't use its own effect while it is still in the deck.