The official description gives the durable rule: find eggs, hatch faster pets, and use speed to reach rarer eggs. Treat every other number as a snapshot until you see it in the live game.
Start with a reachable egg
Look around your current area, pick an egg you can bring home, and hatch it. Equip the fastest pet you actually own. That makes the next search wider without assuming a particular egg will produce a particular pet.
Choose one bottleneck
If you cannot find the rarity you want, look at the radar table. If travel is slow, focus on a faster mount. If a rebirth is close, check its pet and Cash requirement inside the live game before spending.
A repeatable session
Run a short loop, return to hatch, compare the new pet with your current ride, then choose the next egg tier. Recheck patch changes before following any old route.
No guide can guarantee a hatch or a rare egg spawn. The live game panel wins when values differ.