Is it normal for the 12V battery to drop too low to start after sitting for a week? Seems like it should go longer than that. 2012 model 4 with a new Toyota battery.
Not normal at all. I've left ours sitting for as long a 3+ weeks while on vacation. Unless ... you've been making lots of short trips that don't last long enough to get the 12V charged back up. In that case, every trip will run it lower and lower till it's too low to close the relays that connect the traction battery to the rest of the car. And since a new battery rarely, if ever, comes with a full charge, you're starting out with a deficit.
Check to make sure you didn't leave any lights on, or leave a door/hatch ajar. On a brand new Toyota battery, it should last a long time before it drains to the point where the car won't start. My 2015 with a new battery was left for 4 months at a work location due to Covid. When I went to get it, it started right up.
I would check the parasitic draw. It should be around 25 ma when measured in series with the negative battery cable. We have seen 90ma - 400ma caused by obd plugins, hatch lights, aftermarket security systems, bad ecus and even the electric power steering.
Maybe not. Exactly how "new" is it ? Was it fully charged when new ?? (Probably don't know.) Have there been any other "episodes" of draining it down since it was new ? The battery needs to be fully charged and then tested and the charging voltage in the car needs to be tested too. Sometimes even "new" parts fail a lot sooner than they should.