Would it be too forward to e-mail my potential boss directly?

Hello! I work for a university and I am looking to transfer to a different position within my current organization. I applied and I have a friendly relationship with someone in the department I want to work in. I have been very interested in this department since starting with the university(it's the Department of Diversity, Equity, and Inclusion). I applied for a position that opened and emailed my closest connect in the department asking her to lunch. We had lunch yesterday and it went great. We had our typical chat, mostly business with a little personal. She was so excited to hear that I applied and even started giving me tips on what I should say in the interview. I don't even have an interview scheduled yet. The position is an executive assistant supporting the vice chancellor of the Department of Diversity, Equity, and Inclusion. I have met her once when she first started(her role was newly created). She was very nice and down to earth. I go to every diversity and inclusion related event I can go to to make sure my intent to be involved is known. I really believe in the mission of the department. My question is do you think it's too forward to email the vice chancellor directly and ask to speak with her about the position? Or should I wait to see if she contacts me knowing that one of her team members wants me to work there and should could possibly drop my name? Thanks in advance!