As far as I've been able to determine, the full footage has never been released or digitized so you aren't going to be able to find it online. This means that if you want to find it, you're gonna need to do some legwork and find out where it's being held, if it is open for viewing by interested parties, and then make arrangements to travel to the archive to watch it. It is possible that whoever has it would be willing to digitize it for a fee but that isn't a guarantee or even all that likely.

Now why do you want to see the full footage? Because if it's to see more images of the actual battle, according to Mark Harris in Five Came Back what is seen in the short is basically all there is. Most of the footage that Ford and his team filmed was just background stuff focused on the island and the men stationed there, such as the footage of the men and their equipment seen in Torpedo Squadron 8. So according to Mark Harris, of the 4 hours of film that Ford brought back about 5 minutes was actual battle footage and basically all of that was included in the short (though he does not cite this, so it's hard to tell if he has personally seen the footage or if this was taken from descriptions provided by others).

If you are still interested in tracking it down, your best bets would be to ask the National Archives (the footage was recorded as part of an OSS/Navy assignment), the 20th century fox archives (they released the original short), the Lilly Library at Indiana University (They hold John Ford's archives so most/all of Ford's correspondence and many of the materials related to his film career are found there), or the archives of Robert Parrish if those exist (Parrish was a frequent collaborator with Ford and was the man that Ford gave the original unedited film to to keep it out of Navy hands so it wouldn't be censored/pieced out to newsreel companies. Parrish did the initial editing and sequencing for the short before Ford was able to get out to California to finalize everything. Though I've been unable to locate Robert Parrish's Archives with some quick searching, so it's possible his materials have never been donated or purchased). Additionally Mark Harris has a Twitter account so you may be able to reach out to him about it and see if he has actually seen the unedited footage or has any ideas where it might be. All of this is assuming that it is still extant at all. Good luck in your search for it.