Try not to get so hung up on breeding for one particular dragon, even a 4 or 5 star, especially this early in the game.
Even if you do successfully breed that dragon, to get its BP maxed out you’ll need to breed two more duplicates of it, AND the coinage needed will be too much for your max coins to handle (certain rewards will stack beyond your max, like fish/coins from duty chests or anything purchased, at the very least) One of my Epics sits around despite his high tier because he’s stuck at 2 stars. You may find yourself in a similar bind soon after getting that dragon you need.
There is no trick for increasing odds. You might as well be asking us for tips to improve your lotto chances. Nothing you can do will change that since it all comes down to luck, but the more often to try, the more often you “roll the dice”.
You’re going to want multiple Epics and Legendaries down the road, and to do that you need a hardy roster of Rare dragons. Breedery upgrades will help decrease your waiting time, but not until level 30 for your Rares. I’m holding onto two Bombwelters until level 40 when my Epic breeding time decreases from 16 hours to 12. It gives me more time and more breeding chances, and it makes sense to hold off even if I want Sawmaw /now/…
At this point in the game, hybrids are going to be your best friend. Rare hybrids are far more obtainable than Epic pure breeds, and most of the hybrids will have a higher BP and stats than pure breed Rares. Even an uncommon hybrid can take you surprisingly far.