When setting up to play, if the player's starting hand of 7 cards has Luxray with the "Explosiveness" Ability and no Basic Pokémon, that player may choose to use Luxray's "Explosiveness" Ability to set it up as their Active Pokémon.[1][2]
On the same note, since the player technically has no Basic Pokémon in their starting hand, they may choose to take a mulligan instead (shuffling their hand back into their deck and drawing a new starting hand, repeating until they have a Basic Pokémon in their starting hand).[1][2]
Note that players can't build their deck with only Pokémon that have the "Explosiveness" Ability; the deck still needs to include at least 1 Basic Pokémon (cf. Talonflame's "Gale Wings" Ability).[3]
Consider the situation where a player sets up their Active Pokémon while their opponent takes a mulligan; the player may draw a card for each time the opponent does so. If the player draws into a Pokémon with the "Explosiveness" Ability from this, that player may not set it up as their Active Pokémon or replace the Active Pokémon that was already set up.[1]