2035 is 15 years away and not, IMO, an ambitious target. Car manufacturers are already moving quickly down the EV road. It's the vans and lorries which need to catch up. Hydrogen fuel cell powered vehicles are already in production on a small scale but are expensive.
China is investing heavily in electric vehicles. However, at the same time the country is currently building over 100GW of addtional coal fired power stations so there's no benefit (more likely a disbenefit) in terms of CO2 production and the current objective appears to be reduction in pollution in the urban centres.
Regarding the problem of power needed for charging, the vast majority of drivers don't do 200 miles/day on a regular basis. This majority can make do with lower powered chargers for their daily requirements but will also need access to more powerful charging when they make longer trips. Assuming 4 miles/kWh, 50 miles/day and 90% charging efficiency, the daily charging is about 14kWh. This can be achieved using a relatively modest charger (eg 3.5kW for 4 hours). Nonetheless, 10 million vehicles all drawing 3.5kW at the same time is 35GW but that could be easily spread over twice the hours during the night. However, increasing night time demand will eliminate the currently available cheap electricity. Hydrogen production will probably also need electricity but there's potential for storage to minimise power demand when it's scarce.
A related issue is that sooner or later government has to change the taxation system to compensate for the revenue lost as vehicle sales reduce. Road pricing is the obvious solution and this may have the side-effect of encouraging people to travel fewer miles. Ultimately, less travel is what will help the planet. We need to get the politicians to ensure closer proximity between homes and jobs.