Hey Stata Community!

I have a question concerning generating a new variable.

My dataset looks like this:
Product Date
A 05/2017
A 05/2017
A 08/2017
A 08/2017
A 12/2018
A 03/2019
B 01/2014
B 02/2014
C 03/2012
C 03/2012
C 03/2012
C 08/2012
D 01/2017
D 05/2017
What I would like to do is generate a new variable, that tells me the date rank order per product, like this:
Product Date Rank
A 05/2017 1
A 05/2017 1
A 08/2017 2
A 08/2017 2
A 12/2018 3
A 03/2019 4
B 01/2014 1
B 02/2014 2
C 03/2012 1
C 03/2012 1
C 03/2012 1
C 08/2012 2
D 01/2017 1
D 05/2017 2

I already tried "egen" and "rank" as commands, but I never got the numbers I wanted in the rank variable.
I think the problem is that I want to create a rank that is based on 2 prior variables (product AND date). (btw: I have my date variable as numeric and as well as string, if I need to take the other one. So far I worked with the numeric one.)

I would be very happy if someone could help!