Can't keep original file and creation date when transferring photos from icloud?

Where are you seeing the date, via the Finder? There are two sets of metadata at play here: one for the file and one for the image. The Finder can only view the image created date in the column view:

The Info pane for the file shows the file created or opened date.

If you drag the thumbnail to the Desktop or export not as an original you'll get a new file with a new creation date for the file and the image.

Try these tests:

1 - As a test launch Photos with the Option key held down and create a new, test library.  Import some photos and test to see if the same problem persists. Does it? This tells us if the problem is limited to your current library or is more wide spread.

2 - if it still persists create and log into a new, basic, admin user account, Set up users, guests, and groups on Mac,  and see if the problem persists. This tells us if the problem is limited to your user account or is system wide.

Note:  do not launch any 3rd party apps in the account so as to not install any of the supporting files that most create.

If the problem isn't present then your original account has software installed that is causing the problem.  

3 - boot into Safe Mode according to How to use safe mode on your Mac and test do see if the problem persists. Reboot normally and test again.

Note:  if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode.  This makes it act as a wired keyboard as will assure a successful boot into Safe Mode.

When you download from iCloud the embedded photo specific dates set by the camera will be preserved, but not the file specific dates, as the downloaded file will be a new file. If you open the files in a photo editor, you should be seeing the correct capture date. This will only be problematic for videos, as there is no exif standard for the capture date of videos. To see the capture date in the Finder it helps to write the date into the filename, like some video cameras are doing. See Matti Haveri's user tip for examples on how to save the date taken as a part of the filename: Movie dates and Photos.app - Apple Community

MetricHammer wrote:

Is it not possible to make a copy of a photo in icloud that retains the original creation date?

What’s the EXIF data, not the file system metadata? File system metadata is not your friend, and not under your control, and a hassle to use for what you’re trying to do here. EXIF, conversely, is intended for this, and is preserved across file system operations.

No. When you make a copy you create a new file.