How can you tell what time a photo sent via iMessage was taken?
You can figure out what date &amp; time an image was taken1 (and the GPS coordinates of where it was taken2) by saving the image to your camera roll, opening this online metadata viewer, and loading the photo into that tool.
1 This can be manually modified with a metadata editor or be made incorrect by setting the device time to something that isn't the current time.

2 As long as the Location permission was granted by the photographer in their Camera app, and the metadata wasn't manually scrubbed of this (note that it can be made incorrect by a metadata editor too).

Here's a sample result: