Ha, I was so caught up in learning new software that I failed to notice your specification of 2/4. My apologies. I should have caught it.
As your first four notes established the key as GM, the primary notes are G,A,B,C,D,E & F#. Only the C requires playing in the first position. If we play in the next key up (DM) now the C is also played sharp. I am hardly advanced enough as a student to speak with any authority here, but I suspect that many pieces played in DM are therefore played in the second position (often with low D tuning, i.e., tuning the low E string to D). The advantage of course is that it is much easier to reach the fifth fret. Not only can we reach the A on the first string without shifting, but we can easily fret notes that are normally played on open strings. This allows for vibrato or slurs that are not possible on open strings.
It is indeed confusing to play in second position because our initial training causes us to associate notes with fingers as opposed to frets. For example, our minds tell us that A is played on the third string with our middle finger, when what we want our minds to realize is that it is played on the third string behind the second fret with whatever finger is most convenient.
At some point in time we need to morph from associating notes with fingers to associating notes with frets. This is no doubt one reason why Delcamp often has us playing B on the fourth fret of the third string rather than an open second string. This is a necessary step I think to learning the fingerboard. I would therefore encourage you to try again to play in the second position if at all possible. That you find it confusing is, in a sense, all the more reason to attempt it for it forces your brain to think of frets as opposed to fingers, if you catch my drift. This is a very tiny issue at this stage in our development though, but it might give you a bit of a head start when we are introduced to pieces where the music demands that we move from 1st position.