The output of a load cell is not the voltage on a single wire with respect to ground, but a differential voltage between two wires, neither of which is at ground. You can measure that just fine with a DMM of sufficient sensitivity, but you need to be careful when selecting a DAC. Many can do differential measurements, but some do so by reading two lines and then calculating the difference. That's OK for some applications, but not all.
Best is to use an amplifier. But not just a simple op-amp, but an instrumentation amplifier. They can give you gain, as well as properly handle the differential signal from the load cell.