@Miklos Philips in a conventional way we can add a button showing more details. But in my perspective at first upload, we will show a help text(which is widely using in the modern-day apps) saying tap here to see a detailed view. The advantage of this approach is, we can tap anywhere on the progress except cancel and would get more real estate overall. Just think like Also, once a user used to this she/he won’t care about the button or anything(psychology).

But your point is very much valuable and thank you for that. Solutions will be different for different scenarios/users groups. Cheers!!