In our case, same day was 3pm the next day but otherwise it was easy and convenient. You need proof of travel within 14 days of your appointment but it doesn't need to be an emergency
The turnaround times these days are extremely long, in urgent processing it may take around 5 - 7 weeks before you receive your new passport. However, same day passport renewal is available but only reserved for those with urgent travel pertaining to some sort of life or death emergency, and is only available via appointment.
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