Asking mainly because there’s a tool I have use without an API and if I could script something like that it would make my life a lot easier. Just never tried that type of thing before.
Most testing tools make this kind of thing pretty easy. Cypress sits in the page's JavaScript and has access to a Node back end, so when you're not clicking on stuff you can be firing off requests or doing basically anything.
What you might find is that you don't need any fancy stuff though. Maybe look at the download request in Chrome Dev Tools and see if maybe you can just execute a POST command in your language of choice?
Sometimes you can even do these with pure curl. POST the login form, get back the necessary cookie or token, then request the download URL, if it's easily predictable.