MIT did a study on this issue back in 2019. They estimated that the manufacturing of a BEV produces about 80% more GHG than a conventional car. However, most of the lifetime emissions comes after production. The researchers modeled a number of scenarios comparing lifetime emissions (which includes manufacturing) of BEVs, hybrids, and ICEs. They had a difficult time finding reasonable scenarios where BEVs did not outperform hybrids and ICEs. One such scenario is a BEV in West Virginia, where most electricity comes from coal. The BEV was cleaner than an ICE but dirtier than a hybrid. Other than that:
In fact, Paltsev says, it’s difficult to find a comparison in which EVs fare worse than internal combustion. If electric vehicles had a shorter lifespan than gas cars, that would hurt their numbers because they would have fewer low-emissions miles on the road to make up for the carbon-intensive manufacture of their batteries. Yet when the MIT study calculated a comparison in which EVs lasted only 90,000 miles on the road rather than 180,000 miles, they remained 15 percent better than a hybrid and far better than a gas car. https://climate.mit.edu/ask-mit/are-electric-vehicles-definitely-better-climate-gas-powered-cars#:~:text=This%20intensive%20battery%20manufacturing%20means,a%20comparable%20gas-powered%20car.
One factor that Toyota is not taking into consideration is that EV batteries can be refurbished, repurposed, or recycled. Tesla has stated that it does this for 100% of its batteries. One obvious repurpose is to use old batteries for energy storage. Even old Leaf batteries are being repurposed for storage. So the lifetime emissions benefits of electric batteries can potentially extend well beyond the lifetime of the BEV.
The point is that BEVs have the potential to get us where we need to go with emissions so it is probably best to go all out to develop the technology.