Some approaches are made and "manipulated" in such a way so as to have division into classes within a society & to have division into grades between nations. Some are positioned "up" & some are positioned "down". Those, who benefit from such divisions, would like the status to stay as it is & to be legitimized & accepted. The obvious tangible evidence is that , in many countries, the rich is getting richer & the poor is getting poorer. The "pluses" gained by the rich are related to the "minuses" lost from the poor. Reduction of economic poverty without touching the rich does not work in practice. There has to be charity & there has to be just distribution of wealth locally & globally. We cannot eliminate the  words "donor" & "acceptor " from our dictionaries. It is a wrong formula the one in which there are those who are "over-fed" and those who cannot find a piece of bread. This whole world has to undergo overall change because  injustice is a sure recipe for disasters.  

I would say "Yes".

Say Y1 is the aggregate production of 1000 people, and say that 100 are unemployed (poor). If you consider that the 1000 people (with eventual different levels of income) live "correctly", then reducing poverty means to employ the 100 remaining. The real solution is indeed not to increase productivity of those already working (and/or to redistribute income to the 100 unemployed).

"If we managed to create a viable society with 1000 people, then it might be possible to replicate it for 100". Suppose constant returns to scale for example, with 10 firms producing each 10% of Y1 by employing 10% of the 1000 people, what should be the solution ? Of course, it would be to employ the remaining 100 by allocating 10 new workers simultaneously to each firm (under perfect substitution of production factors, if goods are perfectly reproducible, and assuming no problems in terms of skills). Everything equal, everyone gain : more income, more profits, more production.

In terms of feasibility, I say definitely Yes. In real life, things get more complicated for several reasons (as explained for example by Nizar above), but hopefully, it should be possible to do something better.

You are touching a very broad question indeed. There are some answers in my recent book (attached below). Of course, we ought to consider separately poverty of nations and poverty of the poor in any nation. Quite low Income inequality can be found in poor, middle-incme and rich countries but high values only in poor and middle-income countries. If the share of national income for the richest decile is high, the share for the poorest decile tends to be low. For possible options to eliminate poverty see pages 254-263 in my book.

Book Missing a Decent Living for Everyone: Success and Failure in...

Reducing economic poverty will only be possible through a tactical redistribution of national wealth. Definitely an allocation will be made biased towards the poor and hence undermining some benefits to accrue to the rich fellows. Pareto efficiency will not work rather it is the "Theory of Second Best" that will be used to reduce poverty at the lowest possible damage to the rich fellows.

If we assume full employment and that we are at some point in the Pareto frontier it is not possible to increase the welfare (income) of a subgroup of population without decreasing the welfare (income) of some other subgroup. This is the definition of Pareto allocation.

We can certainly redistribute wealth or income and move to another point in the Pareto frontier. Remember from Arrow-Debreu model that each Pareto optimal assumes a given distribution of endowments among consumers-workers.

Now. Can we use some policy to redistribute income and remain in the Pareto frontier? Usually not. We have to move to a second best, and the reason is that we have to use tax-subsidy instruments that distort optimal allocations and usually reduce incentives to work or to save.

These are general propositions that have been established in the 1960s and 1970s by General Equilibrium Theory.