I basically know nothing about OoT speed runs, but I'm curious...
How long would it take to recreate Link's dream at the beginning where he has no sword, shield, or Goron bracelet when Ganondorf blasts him with magic?

I'm not sure I understand the question, you start the game without any of those items.

Yeah so in Link's dream at the start of the game is of him getting blasted by Ganondorf with magic right? In this dream he has no sword, shield, or the goron bracelet. When the cut-scene actually happens in the game after Link obtains the three spiritual stones, the player is supposed to have at least the kokiri sword and the goron bracelet. I'm wondering how long a run would take to make that cut-scene reflect the dream sequence when it actually happens and what would need to happen?

If you're asking what a speedrun would look like to get to the meeting ganondorf cutscene as fast as possible that would be a Child Dungeons run which has end time after collecting Ocarina of Time which is right after triggering that cutscene; it can be found under the category extension board: https://www.speedrun.com/ootextras#Child_Dungeons

None of the existing sub-tabs do it both swordless and shieldless at the same time but if you really wanted to for some reason it could probabbly be done.