[RPG] How long does it take for owlbears to mature?

You can definitely have a hippogriff as a companion--there's even an archetype for it.

But the text is silent on hippogriff egg incubation periods, so it's up to you as GM to decide.

If you're more of a storytelling GM, decide based on what's convenient timing for your game—otherwise known as "it incubates at the speed of plot."

If you're more of a simulation-minded GM, you still have to make it up, but you should find a number that you can accept as sensible. Perhaps research the incubation periods of very large and very small birds to find a ratio or power relation, then scale that up by your estimate of the mass of a hippogriff egg.

Either way, it's completely up to you—they're imaginary creatures, and the game doesn't care enough to say, so there is no higher authority than the GM on this question.

This is one of those things on which D&D bows to the DM's authority over their world. D&D has provided the creature, but not all the details of its life cycle, ecology, mating habits, regional variations, history, origin, etc. ad nauseum. Different editions have given more or less detail on these aspects of creatures, and this is the level of detail 5e has settled on.

So, in a phrase, "ask your DM," since it will vary according to what the DM wants for their setting. In one setting wyverns might be like reptilian mayflies who live only a year and die every winter, while in another setting they can live thousands of years, and in a third setting they have a lifespan similar to cats, etc.