Child universes (inflationary or non-inflationary) are regions of spacetime that disconnect from the original ambient spacetime. In the traditional models within the framework of GUT, a mass threshold of about 50 kg. is present for the child universe formation process. Here we show, using a particular realization of a child universe involving string-like matter, that this threshold can be substantially reduced to arbitrarily small values: production of child universes with arbitrarily small mass threshold is what we call production from almost empty space. Since this possibility has never been clearly recognized, we discuss its properties, relevance and possible refinements, suggesting that this example might be a simpler representative for an interesting, general situation.