Yes! At this time, TikTok, Apple Music and iTunes allow you to request a specific start time for audio previews.
For new releases, on the upload form you can select which portion of your track users hear when previewing your release. Simply select "When the good part starts" on the upload form to specify which part of the track you want available for previews.
If your release is already in streaming services, no worries! You can head to your album page, click on the "Edit Release" button, and then send a request to streaming services to specify which portion of that existing track needs to be included in the preview as well.
Note: preview clip time editing is only available for tracks longer than 1:16. Additionally, previews are only available in 60 second increments.
For example, if you have a 3 minute track, the latest preview time you can select is at the 2 minute mark.
Additionally, not all platforms offer the full 60 seconds of the preview. Depending on which store or service, preview times may range anywhere from 10-60 seconds in length.