Ah yep. Stretchy will do for a NB and up to a few months, you'll then need to move on to a woven for the support. You will not be able to back carry in a stretchy.

The one I am posting you is a woven, but soft enough for a NB.
You can get Hug a Bubs very cheaply second hand, about $40, if you still want to have a look at a stretchy.