Is a comma needed after 'then'?

[Tan Elaine]

He had his breakfast. Then(,) he went to school.

Is a comma needed? Where I live, the teachers think it is obligatory. However, I guess it is not.

Thanks.

 

[Raymott]

He had his breakfast. Then(,) he went to school.

Is a comma needed? Where I live, the teachers think it is obligatory. However, I guess it is not.

Thanks.

No. There is no need for a comma. What purpose would it serve? It's different from your last sentence with "However", which, as you know, does need one to avoid an ambiguous start. I would also rethink the comma after "Where I live".
But if your teachers require it, use it.