<human>: Could you distill the essence of the text into 1-3 sentences?

So if you've read my previous posts, you already know the story. For everybody else, here's a quick conclusion:

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I've met a girl at my university who seems to be quite shy (I myself am aswell) and I asked her out for a date. She agreed and last week we met for a coffee. It was somehow awkward because it was my first date (ever), maybe hers aswell. We somehow got to know each other a little bit, but there were a lot of pauses and we eventually went home because of that (not a good sign, I know). Positive thing was, she already suggested me a good time for this week where we could meet.

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However, today I met her again and conversation-wise it went pretty good. She only had 1.5 hours time, and we managed to talk all the time without any pauses. It felt like I could have asked her questions for at least another hour of conversation when she had to go. (Just for understanding, we went for a simple walk because it was sunny)

The only problem I currently have is that there has been no physical contact AT ALL by now. Neighter me touching her arm nor a welcome hug. It really bothers me because I think it really keeps a lot of distance between us. I am not saying that I expected to kiss her today, but not even touching her once in any way is a bit harsh.

I know that a reason (probably the biggest one) for that might be me being too careful / over politely. I am not sure though how I can overcome this barrier as she seems so far away from me and just hugging her for goodbye somehow seems wrong. She seems to have interest though, as we already cleared a date for next week.

Does anybody have any help or a method how I can overcome the distance (which is feelable in our conversations)? Thanks a lot.
<bot>: I am dating a girl and we haven't had any physical contact yet, which creates a lot of distance between us.