Can you get someone to help you? Maybe try a different style of carry - I use a hip carry with my moby, tho that's for bigger babies who can hold their head up.
If I remember correctly there's another wrap style you can use for newborns that also puts them in the perfect position to nurse.
So I would say see if you can get someone to help you, check too see if baby is too hot when you wear him (This was a problem with my son in a wrap carry) and see if there's a different style of wrap.
Also - I made a great sling style wrap out of a blanket (Found the instructions on youtube). When my boy was that little he LOVED that. Maybe try that too and do the wrap when baby is a bit bigger?
Hope this helps!
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25yo FTM to a Wiggle Panda , student teacher , newlywed