Horrible MDX Query performance

Hello everybody!

I made a query to find the first buy that each client made by each product category. The query works, but it takes over 2 minutes to execute.

In comparison, I made a small store procedure that brings the same result in less than 3 seconds!

I would like to know if there is something very terrible in my cube design, or if there's a better way to query for the same result, or if there's nothing that I can do to make the cube work faster.

My MDX Query:

WITH MEMBER [Measures].[First Activity] AS
	FILTER(
		[Time].[Date].[Date].MEMBERS, 
		[Measures].[FAT]
	).ITEM(0).NAME
   
	SELECT {
		[Measures].[FAT], 
		[Measures].[First Activity]
    } ON 0,
    NON EMPTY
	{(
		[CLIENTE].[Cliente].[Cliente].ALLMEMBERS  *
		[PRODUTO].[Classe].[Classe].ALLMEMBERS 
	)} ON 1
   FROM [SCA]
   

(I create a calculated member in the cube too, actually, this query runs in over 3 minutes. The calculated member that runs in over 2)

This is my cube design(DataSource, Dim Time, Dim Product and Dim Client):

I'm still learning about cubes and analysis services, so it's probable that there is something very wrong with my design. If anyone could point the error, it'll help me a lot.

Thanks for your time.

ps.: I know that the database design is not the best, but that's what I got from the client, and I can't change it much because of the data import mechanism.