Well, I don’t know much about the Suzuki engines, but am assuming it uses a conventional electric choke system like OMC and Merc used back in the day, correct? You mention using “different choke settings” but are you sure the choke is staying fully closed while cranking? You may want to remove the air box cover and physically hold the choke butterflies closed while an assistant cranks the engine.
You mention using different throttle settings, so I am assuming you are not attempting to start the engine at dead idle.
I suppose it is possible that it isn’t sparking during a cold start, but that wouldn’t be my first guess….
I guess it is also possible that the carbs are leaking/flooding a bit while sitting causing the engine to be flooded when you start it cold. I would expect that this would affect its running quality but anything is possible. You may want to try unplugging the fuel line and letting the engine run out of fuel, then trying to start it the next day (after reconnecting and priming the fuel).
Now that I think of it, perhaps the fuel has drained out of the carbs while it sits, resulting in dry carb bowls when you start it cold. So, if you are not priming the carbs properly with the primer bulb, the engine will just crank until the fuel pump has had a chance to fill the bowls….
Always check the basics first….