[twowheels]

Lithium batteries like to be "pre-stressed" a little to work in the cold. Engage the starter button a little, for a short time, to cause some draw on the battery, and then it should be to full power.

Still, considering the design of the starter it may be best to take a cue from the Austrians and consider the e-start to be a "re" starter, using your leg for the first fire in the morning.