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Some vids about arranging on fingerstyle guitar say to figure out the chords first either by ear or through tabs, then to play the melody on top of them. But that seems like too much work. For one, even if I know the chord I'd have to start thinking of the different ways to play that chord all over the fretboard so it could be played next to the melody note I want.

Instead, I thought that chords could be inferred from the melody. For example first I find the melody by ear. Then for each melody note I’d like a chord on, I add a bass note (from 6th/5th strings) that sounds good with it and then add middle notes (from 4th/3rd strings) and eventually the chords reveals itself from the shape I formed.

So I just keep adding supporting notes to the melody until I have my chord. And I keep doing this to find the other chords. Sometimes I don’t even bother to know what the name of the chord is (especially if it’s somewhere in the middle of the fretboard) as long as it just sounds “good” with my melody note. So I was wondering if this is right. Can chords be found from the melody alone when arranging?

No, not if by inferred you mean unambiguously deduced. For example, organists have developed the reharmonization of hymn tunes into a fine art.

Yes, if by inferred you mean finding chords that more or less fit. That's because harmonization is possible at all. Some sequences of chords will fit better (by various criteria) than others, of course.

Postscript: Béla Fleck and the Flecktones' The Star-Spangled Banner is reharmonized so imaginatively that, without a spoiler (as I've done here), few can guess the melody, albeit never disguised, until the conventional harmony returns at "And the rocket's red glare."

It's very style dependent, but yes melody can imply harmony (chords.)

I think a crucial aspect is to not think one note at a time. Look for melodic segments that match common harmonic patterns.

Let's say you are in C major. The melody tone is G. As a single note it isn't clear how to harmonize it. It could be a I or V chord. Now imagine the melodic segment is G F E. It's much clearer the harmony could be V V7 I. Of course it could be harmonized other ways too. But the point is to look for common melodic patterns when thinking about the harmonic implications of a melody.

And of course there are melodies that outline chords. Like a melody of C E G. An obvious harmonization is to just harmonize that with a C major chord.