Depending on how unobtrusive you want the power cable entry to be, the installation video for the Nest cam outdoors says to use a 7/8" drill to get the power plug through the wall etc.
As it is only a low voltage cable, (as the adapter from the AC outlet is connected to the camera power cable by what looks like a USB type connector), my suggestion is that you open the Nest Cam camera unit, take a picture of the power cable connections then un-solder/unscrew (not sure how it is terminated in the unit) and remove the power cable from the camera unit so that you can then feed the power cable from the inside through a smaller hole in the soffit by attaching it to a stiff length of suitably sized draw wire (straightened out coat hanger and electrical tape?)and pulling it through from the outside then re-terminate the cable back in the camera unit as per the picture you took earlier. You won't have 'cut' the cable per se merely disconnected and reconnected it in the camera unit.
No doubt doing this will probably void the warranty but cutting and splicing the cable most probably will as well.
Here is a link the the Ifixit guide on how to replace the motherboard in a Nest Cam camera unit. Hopefully it may be of some help (given that it is the same as the outdoor unit) in showing how to open the camera unit so that you can gain access to the cable connections.
Nest Cam Motherboard Replacement