Two facts, two dimensions, one query, one cube, can it be done and how?
In the Dimension Usage tab click the ... In the cell that is Fact Order and Dim Product. Switch that cell to a many-to-many relationship. 

Then add a Sum measure on the FirstEverOrder column called First Ever Order Count. Also add a Count measure which is a count of rows called Order Count. 

Now create a new calculated measure which is:

IIF([Measures].[Order Count]=0,Null,[Measures].[First Ever Order Count] / [Measures].[Order Count])


Now you should be able to build your report as you have shown. That's the power of many-to-many.