Alternatives to nested dropdowns?

When a user uploads a new document, they have to assign that document to a certain category and subcategory. Our current solution uses two dropdowns for this.

The problem

So currently the workflow looks like this:

  1. User selects category
  2. Options for subcategory are loaded into second dropdown, depending on the selection for the first dropdown
  3. User selects subcategory

However, there's one major limitation to this solution: The user cannot scan all the possibilities at a glance. This means that if they have certain subcategory in mind, but don't know the corresponding category of their desired subcategory, they will need to click through all categories in a trial-and-error manner in order to find the needed subcategory.

Since subcategories are lazily loaded when a category has been selected, there is also no possibility to search through all subcategories. Another stumbling block when it comes to searching is, that there could be equally named subcategories within different categories.

The alternatives

I've read through similar questions here on UXSE and the only viable alternative seems to be a tree view. I don't think there's anything wrong with tree views in general. However, categories and subcategories are created and maintained by admins and thus, not limited in number (note: customers' admins, not ours. So every customer might have their own unique set of categories). So we are dealing with 1..n categories, which each contains 1..m subcategories. Therefore, the tree view could get quite large, making it very cumbersome to read and use.

The same is true for a singular dropdown with both categories and (indented) subcategories.

Constraints

  • Exactly one category and one subcategory can and must be selected.
  • The hierarchy is limited in depth as described. There are no sub-subcategories.
  • Categories are unique.
  • Subcategories are unique within their category, but not globally (There could be an equally named subcategory in another category).
  • No constraints to number of categories and number of subcategories.

The goal

Making it easier and more convenient for the user to select category and subcategory. Especially if the user is unsure about the needed (sub-)category, it would be very helpful to get an overview of what's available.

Is there something I am missing? There must be a clever way to do this. Or is our current solution already the most feasible option? Any input is greatly appreciated!