Physics says no. Our young are smaller than we are because we cannot birth young equal to our own size.
Even your example, the kiwi bird, has an egg 15% of the body weight of the female adult mother.
However, you did say "barring puberty" which means that, really, you could birth a child that's tiny, and it just grows a whole bunch during that time, while for some reason not growing at all prior to that.
This doesn't track in any known biology, even in the example you gave.
I mean, there's some terrible things I can think of, like the baby kills the mom on the way out, because it's so large and takes so many resources to grow, and that the mother would not be able to move at all during most of the pregnancy.
Notice that your example (15% of body weight) is supposed to be a big deal, biologically, so imagine if you upped that considerably.
Maybe you mean something different than how the question is asked? If so perhaps edit it. But, as it stands, this is actually not possible. Insects come the closest to this.