Bit of an ask - I'd need to disable the solar, drain batteries completely (which isn't good for lifetime), and disconnect some of my feeds (I have a solar mini grid on my plot with different houses feeding each other).
You'll just have to trust me.
Essentially if the Sunsynk inverter has no battery no grid and no solar, it will be off.
When it wakes up due to sufficient solar, it will start charging batteries. Once the batteries are charged enough past your minimum set voltage (which could be dependent on type, if you have canbus or other connection etc), then it will be happier.
Dead start is definitely possible., although it can depend on what batteries you have as
@Mike Hoxbig noted above., some BMS's won't start immediately, some will etc.
In my case I used an old unused Dead Acid set to get my Sunsynk up and running. They were unplugged for 2-3 years, and completely dead. I didn't need to do anything other than connect up, and wait for the sun to come up the next day for them to start charging and the Sunsynk to provide power to my mini grid (which is essentially supplement the other solar install as needed at the moment).