The Map module command Map > Tracklog > Set Tracklog Time Offset always shows the wrong starting date/time for a tracklog, 12/31/00 4:00 PM PST (which is represented internally as the number 0). LR 13.1 and prior versions showed the correct starting date/time. Tested on LR 13.2 / Mac OS 14.4.1.
For example, download this tracklog:
https://www.dropbox.com/scl/fi/j76cd3q3aavr3fz8hhnz4/Big-Lake-2023-Tracks.gpx.20234.05.04.zip?rlkey=...
and load it into the Map module. Observe that in LR 13.2, the Set Tracklog Time Offset command displays the incorrect starting date/time:
But LR 13.1 displays the correct date/time: