Let's assume stealth is not part of your situation.
And assume you are parked or camped far away from anyone who would be annoyed by the noise.
You did not include your total solar capacity. But lets further assume you have enough solar to keep everything you are running such as a fridge, lights and fans, plus the monitor and amp and game console.
A 600 watt amp is probably not going to pull it's full rated current all the time, and it might only be rated at 600 watts peak, which means the RMS rating might only be 200 watts or so.
Further assuming, you might have it at half volume or less most of the time, your average current drain might be in the neighborhood of 10-15 amps or so, including the monitor.
We need more information to narrow it down, but these are assumptions that give you a starting point.