Android - How to see at what time an SMS was sent?

Download and install the application "Android Messages" made by Google LLC. This app replaces the standard Message app. To see the time an SMS/message was sent, just push and hold a finger on the message and press on the information icon that appears. In my case (OnePlus 5T, Android 8.0.0) I could even check messages that I had received before I got the app.

Source: https://androidforums.com/threads/text-messages-actual-time-sent.73270/page-2