If you call in late to work, how late is 'acceptable'?

I have an interview.
I have asked if I can interview before or after my work shift.
The answer was no.

My only option is to call in late or call out sick.

My supervisor is very lenient, however because of the short notice , she'd most likely have to run it by the mean manager.

Also, if I ask for my job to make arrangements, and I get [b]denied[/b] and call out anyway, that's a write up.

My shift starts at 8. The earliest I can interview is 9

😕