You could learn a back carry (try back wrap cross carry) with a woven wrap at this stage, but don't use a stretchy wrap like the Moby for a back carry. Despite their instructions, it is not a good option for a back carrier, as the stretch makes it hard to do a good one.
For Ergo, I believe it is once there is really good head support and their legs can be out? How do you know if baby's legs can be out? When you'd carry them on your hips with legs spread and it's ok. If baby is still bringing legs in or squishing them in when carried, then it's too early. Unless your baby is is on the big size, most 4 mos old are too young to spread their legs over a back (maybe hips, but back is even wider).
I could tell my baby could spread his hips wide enough when he was comfortable sitting on my hip while I was holding him. Then, when I could put him in the Ergo on my front and he was comfy with his legs on either side. If they aren't comfortable they'll let you know! I know my baby did!
I like using a MT for a back carry at this age, as I think it's easier to learn than a wrap. I liked the instructions at www.kozycarrier.com when I was learning to do back carries. A tall-bodied MT gives good upper-body support, and the fabric can be squished enough between baby's legs to accommodate in case she's not ready for a full straddle. Try both a high back carry and a regular back carry.
The Beco Butterfly might be another good option. I was able to do back carries with my dd at 3 months in this carrier, where it was more like 5 months before she was ready for the Ergo. The safety harness provides good support for the body, it's got a little more narrow straddle than an Ergo, and it's got a tall body for head support.