Though young budgies bond with humans more easily, it ultimately is down to the personality of the bird whether or not they decided to bond with humans or are outgoing. It seems that Sweet Pea has an outgoing and friendly personality so she will most likely bond with you given time and patience, as well as a lot of interaction.
On the other hand, most budgies do not like to be petted. My girl is very bonded to me and she will not stand for it; most budgies are this way starting in adulthood. Therefore it's important to watch their body language and determine if she's ok with that or not; from what you've said it seems like she's not!
For now since you just got her it's best not to try and touch her or put your hand in the cage. Many budgies are submissive initially because they are very scared in their new home. Even if this isn't the case for Pea, it's best to not touch her for two weeks and instead spend lots of time interacting with her with her in the cage, such as sitting next to her, talking to her, reading to her, talking out loud to her, even if it's nonsense, she will feel like you're including her in your flock. Additionally, if she's fine with it, resting your hand on the outside of the cage is good too.
Eventually I suspect she'll start moving over to the side of the cage where she can see you better
Please keep us updated on how she's doing!