Hi Sjviolin, I will try to assist!
The solo indicates ‘sul G’ which tells us it is intended to be played all on the G string. To do this, you must start in fifth position for the first measure, playing 2, 4, 2, 1…….
Then, shift down into third position for the next measure, playing 1, 4, 3, 1, etc. Then in the third measure, I don’t believe the next section is intended to be continued ‘sul G’, just the opening motif, so I would move to D string in second position.
So after the second measure, where you play in third position on G — 1, 4, 3, 1, then on D 2–2 (here you can move 2nd finger down a half step to play the following 16th notes, all very nicely under the hand, on D string, (sometimes on A), but in a nice position of the hand for this and the next measure.
I hope this helps! Let me know if you need more fingerings for this piece or if you have other questions!