There are two times when we see a transport from the POV of the transportee.

From [Voy: "Prototype"][1] (unfortunately in monochrome due to the subject being a robot)

[![View of the Voyager in space, obscured by an increasing density of white spots until it whites out, then clears in reverse to reveal the interior of Voyager.][2]][2]

And [TNG: "Realms of Fear"][3] (from the perspective of Mr. Barclay).

[![A view of the Enterprise transporter room as Barclay begins to beam out, with an vertical striping effect of white lines from top to bottom that expands into a static-like overlay as he starts to fade out.  From his point of view a snow effect thickens to complete white-out then fades to reveal the interior of his destination.  Finally from the perspective of the terminating transporter the snow effect fades out to leave him standing.][4]][4]


  [1]: https://memory-alpha.fandom.com/wiki/Prototype_(episode)
  [2]: https://i.sstatic.net/yqCKp.gif
  [3]: https://memory-alpha.fandom.com/wiki/Realm_of_Fear_(episode)
  [4]: https://i.sstatic.net/IZ5Hg.gif