How do you design a religion where the "gods" are physical...

How do you design a religion where the "gods" are physical, can die by old age and have interbreed with the human nobility?

Make it so that their godly powers can be passed down or bequeathed to others of their bloodline. Maybe its a magic artifact, maybe its divine power, maybe its just understanding how electricity works, but they have something that only they can do that makes them "gods".

Godly powers are inheritated through blood or the will of the former god

Does Egypt ring a bell?

Imperial China?

Have a look at the deity mythologies of China and the Aztecs for some inspiration.

Greeks too. Zeus fucked a lot of mortal women.

Gods are in fact deified ancestors whose godlike properties are passed to a descendant once the latest bearer dies.

The people of Jotenheim don't see Thor as a god. He is just one of their more talented heroes. They live similar ages and many can accomplish similar tasks on his world.

But drop him on Earth and he lives thousands of years longer than humans and can control forces we still refer to as "acts of God".

Being a God is simply a comparison between two individuals. A squirrel might see people as gods.

Easy.
Incorporate elements of the various real-world religions which taught the Gods walked amongst us.
Then have an eternally changing roster of Gods as new ones are born to take up the mantles of their forebears/

Just because they can die doesn't diminish their world-shaking power, nor the desire of man to worship them.

If humans are made in the god's image, then it isn't farfetched to say that all humans were descended from gods long ago. Each generation inherited weaker and weaker powers until you get the mundane humans you see today and the gods are the thing of storybooks.