MOSFET and 3 V power supply
The first indication of how low Vgs you can apply is the Vgs-th (gate-source threshold voltage)



In this case Vgs-th is 3.2V (max value) so anything below that is a no go. Also note that the Vgs-th is specified for VGS=VDS and ID=250uA, so when you apply Vgs=3.2V, you will get an equal voltage drop across drain-source with a drain current of just 250uA , in other words you can't really use the mosfet with that low Vgs.

To find a proper Vgs, you should check the Vgs vs Rds-on graph and find an appropriate value of gate-source bias that has a drain-source resistance that is low enough for your application.

Your specific device has this graph



so the lowest you can go based on that is a Vgs=4.5V for about 18 \$ m\Omega\$ resistance (estimated values).

There is another graph where you can get info from.



The graph is for VDS=5V so for Vgs=3.9V the Rds-on will be 5V/20A = 0.25 Ohm, if that level of resistance suits your application then you can use a Vgs that low but to get the best of the specific device you need to go higher.