Custom theme – Access wp-content without FTP

Hi there, My company has just purchased a business that uses wordpress for it’s site. I am new to wordpress but understand how to build sites with dreamweaver, html & css. I can usually look at code and figure out what I need to change or edit to get the results I want.

That said I am struggling because my site has a custom theme, but they’ve never had a hosting account anywhere. Is there somewhere I can go to download or access the wp-content without having copies of the original files? I know there is not a file manager or place to access the specific files I am looking for, but is there some other way to download or access my theme?

I have spent the last two days trying to find access via my dashboard control panel. I have also done multiple searches and am still coming up blank. If there is anyone who can advise me on a way to access the root files, wp-content, I would be most grateful.

Thanks for any and all help.