How young can someone be to get sciatica pain?

Any age. True sciatica comes from the inflammation of the nerves in the lumbar spine that create pain going down the leg. If you just have back pain going into the buttock region (not sciatica), that can be si (sacroiliac) joint dysfunction/mechanical low back pain. Any strain of the muscles, tendons or ligaments of the low back can cause regional pain. Ice/heat, stretching, otc Ibuprofen help.
No minimal age. Sciatic pain is pain that goes from the hip, down the leg to the foot. Theoritically it can be seen in any age group, although it is more common once a person is past their teen years.
Any Age. However, typically seen in patients in their 20's and 30's usually at the young age range. I have personally seen herniated discs and sciatica in kids as young as 13. Just depends on what the kid is involved in (if high performance sports activity or lifestyle).