There are a few reasons why your first split, overall elapsed, and/or moving times may be shortened.
There's a known Apple bug where, if you start a recording while the Watch is still connected to your phone, the route on the map appears to start later, and the total distance is shorter than the Watch's unsaved activity summary. What happens is that a few points are recorded in the file pulled from the Phone's GPS instead of the Watch. When the Watch goes outside, and the phone stays at home, it takes the Watch a long time to realize that it is disconnected and that it needs to start getting its own location. To avoid this in the future, start your recording away from your phone if you're going to leave it behind.
If that's not the case, keep in mind that time data is only written to the file after a GPS connection has been established. Strava gets access to the GPS hardware once you've started a recording, so there can be a delay between the start of the activity and when a signal has been acquired. The discrepancy will not appear during the recording, the app will appear to be functioning normally. The issue is only visible once it has been uploaded to Strava. A workaround for the issue is to start an activity outside, wait about 30 seconds, save and discard it, then start a new recording.