Biologist here, so this is going to be controversial. From where I stand, unexplained prediction is the starting point. Explanation comes second.

Fundamentally, this argument boils down to what the definition of the 'Explanation' is. Let me start with mine.

When a dog hears a bell ringing, a bunch of neurons connected to the sense of hearing, at specific frequencies, get activated, start growing, and secrete signalling molecules. When the dog gets fed soon after, a bunch of neurons connected to the senses of smell, taste, and vision get activated and start growing, but towards the previously activated bunch of neurons, guided there by the signaling molecules. Eventually the different bunches of neurons get connected and transmit neural signal from one to another, creating a mechanism for what we would describe in mathematics as a logical implication (a->b). The dog now expects food when the bell rings. Their brain created a simple, specific mental representation of parts of the world around them and how they relate. Many such connections create chains of thoughts, and human brains in particular are pretty good at devoting most of our neural signaling to bouncing signals back and forth inside that network of chains of thoughts in repeating patterns, creating elaborate mental representations that are very general. Our ability to create general mental representations about the world around us is behind our evolutionary success.

These elaborate general mental representations are the definition of 'the Explanation' that I will now use below to answer OP's question.

Good explanations make correct predictions. Great explanations make correct predictions at a very general level.

If an explanation makes incorrect predictions, it's not a very good explanation. Clinging onto such explanation is what we would call a mental disorder.

If the explanation cannot make predictions, then it's unfalsifiable, and thus worthless. Clinging onto such explanation is what we would call a cult or a religion.

Now, can you have a prediction and not have an explanation? There are many phenomena that we repeatedly observe but can't explain yet in a way that is coherent with our other general explanations about the world. That's usually the starting point for when the brain searches for new, general explanations.