OK - I should try to explain a few things better.
A number of old engine ran on Town-Gas (or other kinds of gas) - not gasoline - so no carburator.
Others ran on Oil - like old Hot-Bulb Engines - were the oil was injected into the Hot-Bulb (low pressure) - again no Carb. The Kerosene Engines had somekind of Mixer as you mention.
Starting Procedure ; no two Engines designs has the exact same best practice - but in my experience tells me that it is almost completely impossible to start a cold engine with an open Throttle.
In my youth, I used to slowly open the throttle during cranking, from closed to a bit over fast idle ....
If no succes - slowly closing again. I used to be able to hear when I was close to succes - Electronic Fueling and Ignition, has decreased my abilities over time ....
Unless the weather and Engine is warm - I also expect you to have to use somekind of Enrichment function - like a Choke - for the Engine to fire. Almost all those devices do NOT work if you open the Throttle much over Idle.
As you haven't got the Carburator dialed in for your engine yet - you will have to experiment with the exact Throttle position for starting.
I noticed that your Honda Carburator includes a Fuel valve - I hope that you have it in open position when trying to start the Engine. I mention this as I have never seen any other carburator were this valve is build into the carb itself.
I hope that I'm not telling Granny how to suck Egs
Best wishes
Per