well, since it is a fantasy character, it can be either age. it can be a baby or it can be an adult. i think fantasy characters in movies and cartoons don't have a true age.
sometimes it helps to look at the characters apperance and how it talks. for example, tails from sonic looks and acts like a young fox. if i had to guess godzilla's age, it would be an older adult, maybe around 40 years old.