With a woven wrap, you can safely back wrap your baby from day 1 (if you do it carefully and know what you're doing). With other carriers, it's better to wait until the baby has excellent head and torso control. I started wearing DD on my back in a high back carry with a mei tai around 14 weeks, I think. I'm planning to back wrap this new babe whenever I feel up to it, probably in the first couple weeks.
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And I know you didn't ask about this, but if front carrying is hurting your back, in my experience, a ring sling is going to be even worse. They always feel like they're pulling my back and neck out of whack. It won't be so bad with a little baby though. I have some tips for avoiding back pain during front carries too if you want to hear them! 