This is just a psychological problem. You think you should be "playing the notes with your fingers" but that ignores the fact that you are really using your whole arm.
You didn't mention the jump at the end of bar 2, between the G with your thumb and the G sharp an octave higher with your 2nd finger. If that doesn't cause you any hang-ups, the much smaller jump from A to C shouldn't be a problem either.
The C is the end of a slur, which means it shouldn't be joined "legato" to the next note, and it also have a staccato dot, which means it should be played a lot shorter than the written length.
You just play the C with your thumb, lift it off the key, and then move your whole arm to the left a bit so exactly the same motion of your thumb then plays the A.
Actually, I don't like the fingering given here for the first bar, and similar places. It's trying to fit the fingers on the notes like a beginner's five-finger exercise, but that leaves your hand and arm unbalanced, because the E-A chord fingered 3-5 is slightly stretching your fingers wider apart than their natural spacing (especially for a young beginner with small hands) but leaving your hand "unbalanced," because the thumb is just hanging in mid air.
The wrong way to learn to play the piece with that sort of fingering is to stiffen up your arm and wrist, to stop your thumb "falling down onto the keys" because it doesn't have anything else to do.
A better fingering gives your thumb some "real work" to do, and makes you use your whole arm to play this. Finger the start
2-51 2-51 51-3-2-1 1-2 1-3 | 2-51 2-51 etc.
The "2 1" fingering right at the start is similar to playing a scale where the 3rd or 4th finger is on a black key followed by the thumb on a white key. To add the 5 on the A, the natural movement is to rotate your forearm, so your hand pivots around the 2 and your 5th finger moves down to hit the key. This is the basic "forearm rotation" playing technique.
It might feel strange at first, but once you get used to the idea, it gets your whole arm moving freely. As you progress that will lead to much less playing fatigue, because you are using the big muscles in your upper arm and shoulder to do the work, not the small ones that move your fingers.