Not sure about migratory birds in particular. But being able to survive without food for long periods is clearly a good trait. It has evolved across plants an

Not sure about migratory birds in particular. But being able to survive without food for long periods is clearly a good trait. It has evolved across plants and animals to a lesser or greater degree. That trait can team up with another. For example an animal that can dig can hybernate underground. An animal that can fly can journey to find food or a mate. It may start by flying a short distance across land and slowly build up the distance over successive generations. Then it could learn to follow the coast to find better food. Or develop abilities for navigation. Or an instinct to fly when the days get short and be less distracted by food. Slowly but surely the benefit of flying outweighs the benefit of staying at a food source. The travel gets longer and longer until it is crossing thousands of miles.