Count customers by category of first purchase

Hi there,

I'm trying to be able to count the number of customers who came in and purchased something from a given category, knowing that most customers have made several orders later.

Doing research, I know that I can pull the earliest order date by using { FIXED [Customer ID] : MIN([Order Date)])}, but I want to be able then effectively do a lookup of what category that purchase was in.

I think I can do this via table calculation (Finding the Date of First Purchase or Occurrence | Tableau Software), but we have thousands of records so I'm just hoping to find a count of people based on the category of their first purchase.

Very simplified example of what I'm hoping to do is attached.

Thanks so much!

Kirk