The answer to your question (as expressed in the title) is "No".
Any melody can be harmonized with a wide variety of chord progressions. You can use this to achieve a variety of sophisticated musical effects. One simple example would be using either a minor chord progression or a major chord progression to harmonize the same melody.
That's what makes music so interesting.
It's a well-established songwriting and compositional technique to take the same melody and harmonize it differently each time the melody is repeated. That is one form of what we refer to in classical music as a "theme and variations".
In jazz, it's call "re-harmonizing" or "using chord substitutions".
Now I don't mean to imply that you can take a given melody and choose chords at random and call it a chord progression that accompanies the melody. There are rules for this, and to learn them, you need to study music theory, or at least to listen to some good music composed by people who know their music theory.
Nobody here has yet raised the subjects of harmonic rhythm or counterpoint.
Do you want to compose a different chord for each melody note, so that the chord progression incorporates a distinct bass line? That is called a chorale harmonization in homophonic texture. For example, that is the way that Protestant Christian hymns are often arranged in traditional hymnals.
Or do you want to simply create one chord per measure, or a different chord only on strong beats? In that case certain notes in the melody are treated as notes that are not in the chord, and go by various terms such as non-chord tones or passing tones.
Then there is counterpoint, in which there are multiple melody lines going on at the same time. The song tune is the dominant melody, but there are other lines going on underneath it or around it. In properly composed counterpoint there is still a chord progression that can be perceived and derived by looking at how the notes in the various melody lines line up vertically. Counterpoint is a complex and advanced compositional technique.