UPDATE: A friend invited me to play a board game with 5 other people and guess who was also there.
I acted totally non-clingy, teased her, made people laugh, acted the same towards every people in the room (not chasing her or showing affection towards her) and it looked like she enjoyed it. Then we had to catch the metro and it was only me and her. A perfect chance for isolation and the time I have been waiting for.
No physical escalation because last time, she told me she is not the girl to take home so I wanted to show her it's more than physical. I built some comfort with DHV and fun stories, made her laugh and really enjoyed my time with her without thinking about the outcome. It was actually what I have been expecting for the whole time.
On the other hand, she received texts from someone else twice through the evening and when she saw the message, she told me "Oh, someone likes me.". I took that as a jealousy test and did not react like an AFC. I just replied "Oh, it's good you have someone to call you. You told me you had no one to call you before. That's an improvement!

". There was this one guy who was hitting on her at the same time so I guess I have a competition.
As we were leaving, I suggested that we meet one hour before the birthday party and she agreed unless a friend might need assistance with the party and she does not know her exact schedule. I said "Cool, then I will give you a call during the week and see." and then we left with a hug again. (I'm also afraid that too many hugs will leave me in the friend zone.)
I appreciate if you provide comments on this. They actually help a lot for me to improve.