The correct phrase is "I strongly believe that..."
The reason why is because "believe" is a verb; it is not necessary to add the verb "am" to the sentence.
In English, we often make phrases combining the state of being verbs (am, is, are, etc.) with a gerund (drinking, thinking, doing, etc.). For instance, you would say, "I am drinking a soda" or "I am doing my homework." We typically use this structure only to describe actions in progress or that are currently happening.
Since your beliefs on a topic are unlikely to change, we do not use the combined state of being and gerund to describe this. "I am believing" sounds unnatural. "I believe" or "I strongly believe" are the correct ways to say this.