First, You might get lucky with the AUX START button instead of the Ignition switch, Works on my house.. So does a jump box but that takes knowledge of where to hook it.
Next. And this is the important stuff.
Run that generator at least six hours, Depending on your converter may take 8 or more but at least six houirs
THEN shut down and using a digital voltmeter, wait 20 minutes and measure battery voltage.
Home is where I park it!