If you are asking about activity data, starting with iOS 11, there is now support for Apple Health data to sync to iCloud. Check your iCloud settings to make sure that syncing is turned on.
That should do it even if you set up a phone as new. That said, I have never switched phones, but my activity data was available when I set up my phone as new without restoring. (Watch faces and layouts and app installs, though, I had to re-do from scratch.)
That said, I would unpair your watch from your current phone if you can and make a backup to iCloud or iTunes (encrypted to iTunes or the health data will not back up) and then, if you find that health data did not sync, then restore the data from backup to the iPhone SE.