You're talking about going from animal traction to electric motors without the heat engine which is a large conceptual leap but not impossible. The two biggest problems are that:
- Without coal fired copper refining processes building the infrastructure to generate, let alone transmit, the electrical power that you need to refine the lithium, cobalt, etc... to make the jump to long range battery systems will be next to impossible.
- Coal and oil were being used, in isolated areas on a small scale and not usually burned in the case of the latter, by the iron age.
The only solution I can see is a VERY early harnessing of electricity, the late bronze age or earlier; wood is the direct source of all industrial fuel, gold, copper, and it's alloys, are the only widely used metals and extremely good conductors.
An early culture that revered the thunder and sought to understand it's companion, lightening, could build a working Van de Graaff generator, they're not mechanically complex even though they came rather late in our exploration of electromagnetism. From there using animal power and, eventually, wind and/or water to turn the crank is not a big step. Once you have abundant chained lightening experimenting with it's effect on anything and everything is a natural outcome of human curiosity. I would expect someone to work out reliable, though not particularly efficient, electro-reduction (practically not the principles behind it that is), especially of copper and tin, within months of the first reliable generator going online. The shift to magnetic dynamos (which are also electric engines if you reverse the current flow) is a challenging step to work out in a society so radically different to our own but assume it and you have efficient electrical generators that rely on renewable sources of kinetic energy and a society that relies on electricity, rather then thermo-chemistry for all it's industrymetal refining etc...