Is it possible to add missing <CreateDate> tag?

[nikmgl]

I have been searching the forum but could not quite figure it out.
Here is the result from

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exiftool -s -time:all on one of the files that I am having problem with.
FileModifyDate                  : 2019:05:31 10:48:27+03:00
FileAccessDate                  : 2022:06:27 11:41:12+03:00
FileCreateDate                  : 2020:07:11 11:23:10+03:00
ModifyDate                      : 2019:05:31 10:48:15
GPSTimeStamp                    : 07:48:15
GPSDateStamp                    : 2019:05:31
GPSDateTime                     : 2019:05:31 07:48:15Z

I am guessing this image file does not contain <CreateDate> tag. As I am moving/sorting all of my photos using <CreateDate> tag, I want to add it to the files that are missing this tag. Is it possible?

[StarGeek]

Yes you can.  The very basic command would be to directly set it
exiftool -CreateDate="2022:06:27 12:00:00" /path/to/files/

But hopefully one of the existing time stamps will be what you want.  From that output, it looks the ModifyDate might be the one you want to copy from.
exiftool "-CreateDate<ModifyDate" /path/to/files/

These commands creates backup files.  Add -Overwrite_Original to suppress the creation of backup files.  Add -r to recurse into subdirectories.

[nikmgl]

Thank you @StarGeek.

I should have mentioned it in my OP, sorry. When I try  -CreateDate<ModifyDate or -DateTimeOriginal<ModifyDate I get following error:
no writable tags set from ./

[StarGeek]

What is the exact command and output.  Copy/paste the command and output here and use the Code Button to format it.  Also, is there any pertinent data, such as running the command from a batch/script, as well as the OS and shell you're using.

Otherwise, all I can say is that it works here

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C:\>exiftool -time:all -G -a -s y:\!temp\Test4.jpg
[File]          FileModifyDate                  : 2020:07:11 01:23:10-07:00
[File]          FileAccessDate                  : 2022:06:28 07:41:16-07:00
[File]          FileCreateDate                  : 2021:09:07 07:41:30-07:00
[EXIF]          ModifyDate                      : 2019:05:31 10:48:15
[EXIF]          GPSTimeStamp                    : 07:48:15
[EXIF]          GPSDateStamp                    : 2019:05:31
[XMP]           GPSDateTime                     : 2019:05:31 07:48:15Z
[Composite]     GPSDateTime                     : 2019:05:31 07:48:15Z

C:\>exiftool -P -overwrite_original "-CreateDate<ModifyDate" y:\!temp\Test4.jpg
    1 image files updated

C:\>exiftool -time:all -G -a -s y:\!temp\Test4.jpg
[File]          FileModifyDate                  : 2020:07:11 01:23:10-07:00
[File]          FileAccessDate                  : 2022:06:28 07:41:52-07:00
[File]          FileCreateDate                  : 2021:09:07 07:41:30-07:00
[EXIF]          ModifyDate                      : 2019:05:31 10:48:15
[EXIF]          CreateDate                      : 2019:05:31 10:48:15
[EXIF]          GPSTimeStamp                    : 07:48:15
[EXIF]          GPSDateStamp                    : 2019:05:31
[XMP]           GPSDateTime                     : 2019:05:31 07:48:15Z
[Composite]     GPSDateTime                     : 2019:05:31 07:48:15Z