Choose a comfortable assignment
Begin with one chord you can hold easily and a short pattern across three or four strings. You might use the thumb for the fourth and third strings and fingers for the second and first, but there is more than one workable assignment. Choose one that keeps the hand relaxed and the notes consistent. On a high-G ukulele, remember that the fourth string is not the lowest pitch. Listen to the actual contour rather than assuming the pattern behaves like a guitar bass-and-treble figure.
Make each note intentional
Pluck slowly and compare the volume of the notes. A stronger thumb can overwhelm the upper strings even when it is not producing the lowest sound. Reduce force before asking the fingers to compensate with a harder pull. Keep the motion close to the strings and count the subdivisions aloud. Practice the pattern on one chord until you can listen to its phrasing rather than monitor every finger. Then add a second chord with an easy transition so the fretting hand does not obscure the picking lesson.
Adapt the pattern to the phrase
If a chord changes before the picking sequence finishes, move to the new harmony at the correct moment. You can shorten or vary the sequence rather than forcing every measure into the same loop. Check the progression in AudioChords and listen for the chord timing in the recording. Try leaving a small space at the end of a vocal phrase or emphasizing one upper note as a gentle response. Fingerpicking becomes an arrangement when its timing and contour support the song, not merely when you can repeat a memorized order of string numbers without stopping.