Is this dialogue OK?
Person A - Did you get to school on time? / Did you arrive at school on time?
Person B - I arrived after the class had started. / The class had started when I arrived.
I arrived after the class had begun. / The class had begun when I arrived.

Question

Is this dialogue OK?
Person A  - Did you get to school on time? / Did you arrive at school on time?
Person B  - I arrived after the class had started. /  The class had started when I arrived.
                    I arrived after the class had begun.  /   The class had begun when I arrived.

Answer

They are all fine, except I would add 'already' to these two sentences to make them sound more natural..

The class had ALREADY started when I arrived.

The class had ALREADY begun BY THE TIME I arrived.