Okay, bear with me because I am also learning Spanish but this is my understanding:
Spanish-speakers generally don't use "Estoy hambre," only "Tengo hambre."
"Hambre" is a noun. So, if you were to say "Estoy [I am] hambre" that would be almost like saying, "I am SO malnourished that I have turned into hunger itself." ¡Qué dramático!
If you wanted to use "estoy," you could use "hambriento," to change the noun into an adjective. But, I don't think anyone says it that way.
"Tengo hambre" means, literally, "I have hunger." That is just the way people say it.