Yes you can use the Schwarzschild argument. Expanding space is only a handwaving rationalization, a coordinate-dependent way of thinking that is not compatible with the principle of general covariance.
If the gravitational source density was ever more than zero, then it follows that the contents of the universe were less massive in the past. In an inertial set of coordinates, not the screwy Freidmann coordinates, it can be understood that the shards of the Big Bang, flying apart at next to lightspeed, still add mass to the universe today, but at a diluted density.