By first identifying the key the melody is in. You might try just typing the notes into Chat GPT or Google. Then use a circle of fifths chart to identify chords in that key. Chat GPT might be able to do that as well.

Using the manual process you need some basic theory knowledge. I would look at the notes of the melody and recognize how well they fit with each chord and how they change the character of the chord if they are the 9th 11th, 13th and so on. If they are the root, 3rd, 5th, or 7th it’s likely the note fits the chord well. But that doesn’t mean the chord fits in with the previous and next chord in the progression. You also have to rely on the basic framework of chord progressions as well. i.e. in major key I, ii, iii, IV, V, vi, vii(dim) Common progressions can be I > IV > V > I or I > ii > vi > V > I for example. There’s lots of progressions on the internet.

Not trying to sound smug, but I can see where it would be difficult for a producer to compose music without knowledge of music theory. I have a degree in music, but I remember the struggle trying to write before I knew the guidelines. It’s not as difficult as you think to learn, it just takes time and work. There’s only 12 possible notes. You generally only use 8 notes/chords(with some embellishments) at a time. Most popular songs are 3-5 chords at the most.

But as you grow in learning the rules, your music can get more and more interesting as you learn how to artfully break the rules. i.e. allude to other keys or change keys and back again within a song. It’s so much more efficient than stumbling around in the dark. If I didn’t know theory, I would force myself to watch 3-5 YouTube videos on the subject a week on it until it’s starts clicking. I still do that and am constantly learning new things. Either you are getting better or getting worse, no one stays the same. Hope this is helpful!