Recording timestamps to SD card

I'm wondering if there's a way to write a timestamp (like datetime) to the SD card at the beginning of a recording. For context, I need to do a study in which subjects will be wearing the device continuously for a few days except for showering, so I assume they would need to restart recording each day after showering. I already have the PROG button programmed to start recording to SD card when pressed, but ideally at the beginning of the file, I would document when the subject started the recording. Right now I can get the delay using millis(), but I don't know what time that is at.