What is the minimum required time in service for an E-9?

I see you're in the Army, and the subject is an excellent opportunity for you to learn not just the answer, but how to find it. So lets not just hand you a fish, but teach you how to fish.
AR 600-8-19 is the current regulation that will hold the answer you seek.
The Army Publishing Directorate has an electronic library of most all regulations...and is an excellent resource. http://www.apd.army.mil/
http://www.apd.army.mil/pdffiles/r600_8_19.pdf
SFC though CSM are promoted though a centralized promotion board. Time in service remaining are a regulatory requirements.. As is the bear minimum time in service (17 years for SGM) However DOR and BASD (PEBD for USAR) requirements and other eligibility criteria prescribed within are announced in the board message, and very based on the pool of eligible SM in general and the number of elgible specific the board DA HQ) wants to look at for promotion.

Setting your goals now? Very nice.

The only time in service requirement is that you must be an E-8 for a certain period of time. I made E6 in about 4 and half years.

Speaking from the Navy perspective: If you come in as an E3, you only have to spend 6 months as an E3 before testing for E4 (provided you have a rate).

E-3 to E-4: 6 months
E-4 to E-5: 1 year
E-5 to E-6: 3 years (minimum 2 with Early Promote)
E-6 to E-7: 3 years (minimum 2 with Early Promote, then test for board)
E-7 to E-8: 3 years
E-8 to E-9: 3 years

The way I remember BUPERS, Chiefs are not eligible for Early Promotion consideration.

I have seen people make E-7 within their first enlistment. There are always random circumstances as well that lead to super early promotions, though they are usually rare.

http://www.public.navy.mil/bupers-npc/reference/instructions/BUPERSInstructions/Documents/1430.16F.pdf