Just to be clear, are you asking for advice on how to make a fast explore farming team? I’ll assume you are to start.
The best and fastest explore teams usually require a few traits to really work well.
The bombot teams usually require a fully-traited Princess Elspeth (and probably a fully-traited Mechanist hero class) to be fast. That is a big investment for a newer player and is probably not worthwhile.
Firebomb teams also need some traits, but because Firebomb is a common troop, it only takes one arcane rage stone (plus various lower traitstones) to get Empowered - his most important trait. If you have multiple copies of Firebomb, the strategy is usually to put something that does significant damage up front with Firebombs behind. With the empowered trait, you don’t need to collect mana. You can just cast the firebombs starting with your first turn. Each one will do damage to an opponent and by exploding red gems, you will collect random mana from the red gems exploded plus the random gems around them. You want the firebombs at the back of your team because they will soak up any red mana collected before they die.
The most common troops to put in front are Sunbird (which uses red, does significant split damage and regenerates to full health and armor each time you cast), Rowanne (who does good split damage, boosted by her armor), Forest Guardian (who, when fully traited, can give Sunbird half starting mana), Ogryn (who boosts all stats on all red troops by 5 when fully traited).
Various things can help to make the firebomb teams fast, but most require a significant investment in arcane stones. Getting Firebomb his 3 traits and levelling him up as far as possible is the first step. If you have that, maybe try Rowanne, Firebomb x3 and see how that goes. If you have something that uses red mana that won’t block Rowanne (Sunbird is perfect), you may want to put that first, then Rowanne and 2 firebombs. Rowanne’s damage depends on her armor, so you don’t want her taking any random skull hits while you are using up your firebombs.
Edit: I see from another thread that you have TDS at level 19. He would make a pretty good first troop to go before Rowanne. He’ll absorb the red and purple mana from the explosions while Rowanne picks up the blue and green. If you’re able to fill and cast both, you should easily clear any normal explore.
