"وِلاية كاليفورْنْيا مُمْتازة."
Translation:The state of California is amazing.
Well, first ممتازة means excellent rather than amazing (Amazing is مذهل), also saying "California is excellent" or "California state is excellent" should be correct
Because in Arabic, a definite noun (معرفة) can be achieved using different ways, using "the" (ال) is just one way, another way is being a (علم) or a known thing, such as the name of a person, a country or a state e.g. California.
Another way (which is the answer to your question) is by being associated with (usually before) another definite. The state (ولاية) is a definite because it's associated with (before) California which is a definite because it's a known place, so you don't need "the" (ال).
Just think of it as "California state" rather than "the state of California".
Just to be clear, using الولاية as you said is incorrect.
Other similar examples include:
The city of Berlin -> مدينة برلين
Ahmed's char -> كرسي أحمد
The city's park -> حديقة المدينة