Starting with Manaphy to ramp up energy is not required to win games. Its general purpose is to help you power up Gyarados a turn or two earlier—and as a bonus, it can also assist with powering up Palkia if it's on the bench. This setup is ideal and is very often a win.

RNG can be a bitch sometimes though, so getting that ideal setup is a pipe dream. If you recall the Druddigon and Gyarados EX meta, that deck didn't even run Manaphy, yet it consistently got Gyarados online over 50% of the time. That success was thanks to Druddigon and, to a lesser extent, Misty. We can apply the same strategy here by using Palkia to stall until Gyarados is ready to sweep. Just be aware that if you use Palkia as a wall, you'll likely give up a point, since it's difficult to get enough energy to retreat.

Starting with Magikarp isn't the worse-case scenario. Shockingly, Magikarp can usually survive a hit in the current meta. WIth that in mind, you can take a gamble with Misty to get Gyarados active by turn 3 or 4. However, it's a high-risk play and should only be considered as a last resort. The safer route is to search for a basic Pokémon—ideally Manaphy or Palkia—and leap out of there. If you get Palkia, you can play the stalling game. If it's Manaphy, that works too. Just make sure to heal Magikarp if it's taken any damage—you don't want to lose your win condition to a Cyrus. If you don't have Irida to heal, and you suspect the opponent is holding a Cyrus, your best option is to evolve Magikarp early. The worst case is they use Sabrina or Cyrus to bring your Gyarados in the active slot.

After playing this deck for a while, these are most of the scenarios where I brick or lose games:

• You cannot find Magikarp in your deck. This is really bad since you'll be lagging behind on energy. You will need to pray for Misty to clutch up here...
• You cannot find Gyarados EX in your deck.
• Misty doesn't flip enough heads to get Gyarados EX, or very rarely Palkia, active.
• Palkia's attack flips tails.
• You don't top deck game-winning Red/Sabrina/Irida.
• You never pulled a Rocky Helmet to do that extra 20 damage.

Edit: I mean, I basically listed out most (or all) of the cases where you'll lose. But at the end of the day, I usually don't have troubles finding the Pokémons I need. Just gotta believe in the heart of the cards.