When you create a new route on Strava (web version) it does display some more popular segments on the route preview page. But the full list of segments is only visible when the route is completed and uploaded as a ride. Here is a little workaround to check all segments on a route before riding:
- Create and save a route.
- On the route page click Export GPX and save the GPX file to your desktop.
- Go to https://gotoes.org/strava/Add_Timestamps_To_GPX.php and upload your GPX file.
- Leave all the setting as they are and download a modified GPX (with added timestamps).
- Go back to Strava, click Upload Activity button in the top right, select File and upload the modified GPX file you just downloaded from gotoes.org
- Give the "ride" any temporary name, set activity Privacy controls to Only You and click Save & View
- On the Ride page, you will now see all the segments. Preview and star them as required and then delete the fake ride from your Strava.