Keeping date of original recording in converted video file

I have some video files that came from a digital video camera. If I examine the file using exiftool, I see an output that includes:

SB-iMac(~/Movies/trial) % exiftool f1.dv
ExifTool Version Number         : 12.40
File Name                       : f1.dv
Directory                       : .

File Modification Date/Time     : 2024:05:19 12:26:08-04:00

Date/Time Original              : 2009:01:18 11:28:30

After converting with Handbrake and selecting "passthrough common metadata", exiftool reveals:

SB-iMac(~/Movies/trial) % exiftool f1.m4v
ExifTool Version Number         : 12.40
File Name                       : f1.m4v
Directory                       : .

File Modification Date/Time     : 2024:05:19 12:26:08-04:00
File Access Date/Time           : 2024:05:19 12:26:08-04:00

The Date/Time Original field does not appear in this listing of metadata for the converted file. If I load both files into FinalCutPro, the original file appears as 'its own event' dated 'Jan 18, 2009' and the converted file as an event for 'May 19, 2024'. Within FCP, I cannot find that the revealed metadata for the original file includes the date in 2009. I tried to create my own view of metadata in FCP and selected the 'Date Time Original'. However, even that option does not reveal the 2009 date.) Is there a way of keeping the earlier date in the file conversion process?