You got several strikes against you. Unless you got recorders with good quality timebases (I don’t. Mine are junky USB recorders) you can’t start with an external player and “put the times back in.” At least not easily. And strike two, MP3 is not the celestial gift for timing and precision. We advise—constantly—never do production in MP3.
This dance gets a lot easier if you put in “Camera Marks” at the beginning and end of the recording during the recording. You know that person who stands in front of a movie camera with the clapboard?
They’re not just being adorable. They’re there so the sound and picture people can get back in sync weeks later.
And they’re not in MP3.
I would grade fixing this in post production zero.
In the current release version of Audacity you have to do that manually.
In the next release version there will be a setting in Preferences to customise the default name for recorded tracks, including an option to add the date and/or time that the recording starts. This feature is described in the “alpha manual” here: http://alphamanual.audacityteam.org/man/Recording_Preferences