Does the pump start in other circumstances- like from a genset or the grid? might be a marginal starting cap.
the 12-2 might be a factor, but I think not the only one Going up to 10-2 might help in situations where there are lots of marginal conditions.
you say the inverter cables are 2/0, which is nominal; you might want to step up to 4/0 or double the run of 2/0 . . . just so the drop across them when the inverter goes into surge isn't a factor. what size are the battery interties? They should be the same size as your output lines.
Someone else already asked, but again: is the inverter MSW or pure sine? Modified Sine Wave can be rough on motors and capacitors, so if your motor used to start and now does not, that might be a cause. MSW inverters can also have a hard time starting a motor. How old is the inverter? could it have suffered some abuse that has reduced its capacity? How is it cooled? A hot inverter won't pull as hard as a cool one.
what else is running on the inverter? do you have a large load? or is the inverter lightly loaded? Sometimes with a marginal inverter, calling for a little power before trying to start the pump will get the powerfactor into a place the motor likes better.
In troubleshooting, it's often the case that your first instinct is wrong; (I know mine often is) So the only way you'll solve such a problem is by rigorous application of logic and the scientific method. Pick a portion of the system (the motor itself, say) and isolate it: Does it start on another power source? Does it sound right? (no? does it spin easily and smooth by hand?) is it trying to start under load, like maybe a check valve is stuck open or (rarely) shut? can the pump start with the pipes disconnected? is the pump aligned properly with the motor shaft? has water gotten into the bearings/windings? are the connections in the junction box clean and tight? Is the pump mechanically sound- good bearings, no drag, etc.
then on to transmission lines- the 12-2. Corrosion on connections? connections tight? heating anywhere in the line? voltage sag? will a different motor start and run under load when connected in place of the pump?
then to the inverter: heating up? corrosion? tight connections? voltage sag under load? does it sound good/right?
and then the batteries: electrolyte levels? corrosion? right temperature? age? interties too small, heating or corroded? Charging properly? weak cells?
