While it's okay to be ambitious, it's also important to respect the hiring process and staffing decisions of a potential employer. If they advertised a position, and you applied for it, that is the position they are considering you for. If there had been another open position which you were more interested in, it's fair to mention that during an interview - but it doesn't sound like that's the case.
However, that doesn't mean your hopes of being a manager are a lost cause. Many employers like to promote from within, and some even have dedicated programs to help people transition into manager positions. So, while it may be a little late in your current process to consider this, you can always take advantage of the fact that hiring processes are meant to be a two-way street: employers will evaluate your suitability for their position, and you have the opportunity to evaluate whether they will be a good fit for you.
If promotion opportunities are important to you, or you have a career track in mind, it's worth bringing that up during the interview. While it might come off as awkward if you ask, "can you hire me as a manager instead?" you may get a good answer to a question such as,
I am looking for an employer that I can grow with. As such, promotion opportunities are important to me. Can you discuss your company's approach to internal promotions? Do you have a practice of promoting individual contributors to management roles?
Some employers may balk at this (they may see you as a flight risk if they perceive you're looking for something bigger than the role you applied for) - but that's not inherently bad news, because it sounds like that kind of employer would be a bad fit for you! Other employers may enthusiastically respond about how they have a culture of helping people transition into management roles. That's the company you want to work for!
So - if you are already feeling interested enough in this company to pursue the job, even though it's not a management position, you may want to send them a follow up question to clarify if there are promotion opportunities. But keep in mind, they're hiring for the advertised role - so, if you really want a management position, it sounds like you may be best off abandoning this opportunity and only applying to manager jobs.