We used a Close Baby sling from very early on in our daughter's life. I would NOT recommend a backpack sling because you want to have immediate access to your baby and be able to see if they're getting into trouble, but I assume this kind of thing is what you meant.
The straps are designed to support the head, which assuages your concerns about head support. As it says on the site, it's suitable for any babies over 5lb (2.27kg), as long as you choose the right position. (As a bonus, my partner found she could feed the baby in that position)
Critically, the manufacturer's guidelines are not a replacement for observing your child. I found that initially, you still couldn't do too much with my daughter in the sling without worrying that she'd gone very still (every time it turned out she'd fallen asleep), as the straps neatly hid her head, and tiny babies sleep silently. Similarly, if she'd seemed uncomfortable or struggling, or if the sling wasn't holding her closely enough, then that would have been the point to stop for a while.
As she got a bit bigger, and we stopped (irrationally) worrying so much that she'd just suddenly decide to stop breathing, you find that, depending on the baby, you can do quite a lot while they're in the sling.
Finally, as an aside, you need to be aware of the limitations of on-person carriers vs strollers. Specifically, that when on the go, you cannot put the baby down to do something. If you're sitting down or get tired or sick while out, you can't put the baby down, and this limits what you can do. (e.g. if you need to vomit, you're really in trouble). We found our stroller invaluable, especially as she got older and thus BIGGER and more curious. An 8-month old struggling to get out of your backpack is a very different thing than an 8-month old struggling to get out of a stroller.