Momentum is not a thing that is, it is a relationship we define, and we do so only because it has been shown by experience to be useful in solving certain calculations. Until you understand that concept you will continue to miss the whole point about physics.

There are very few things we can measure directly in nature. They include mass, location, and duration. We have noticed that several mathematical combinations of these measurable things give quantities that are strictly predictable in physical interactions. So we define these properties in such a way that they can be used as "checks" on our theories. Momentum is one of these things. Energy and action are others. We define momentum as a vector, the product of mass times velocity in a certain direction. This is purely a mathematical game, invented by Newton over 300 years ago.

The wonderful thing about momentum is it never changes in a closed system. It's not magic, we rigged it that way deliberately to fit the facts we observed in nature! In fact, there are many other mathematical quantities involving physical reality we could define which we do not bother to, because they are not useful in guiding our calculations.

Well, photons have no mass, and they always have the same velocity, so there is little reason to believe they should have a momentum. But as it turns out, when they interact with ordinary matter, they ACT exactly AS IF they had momentum. When we measure this momentum it ACTS as if it was the product of the photon's frequency and a number we call Planck's constant, with the directional component defined by the photon's velocity vector. So that's how we define photon momentum. Nature sometimes does certain things. Sometimes, if we're lucky, we can come up with a mathematical shorthand for this which allows us to predict what will happen. There is no magic, things just happen a certain way, and some things don't happen. It is the task of physics to find out how, not why.

Momentum is a mathematical property, like pi. It's not something you can put in a bottle or produce in a factory.