Check for restricted air intake. Look at choke operation. Possible leaking reed valve not allowing crankcase compression. Same for crankcase seal.
It's usually easier to get some mix in the air intake so you don't have to disturb the spark plug - try a little more fuel - most 2-cycles like it wet when cold. Usually you can snap off the carb cover and the air intake is right there with a screen in it.
These things can be pesky because newer ones are set to run so lean that its very hard to start them. If you can verify running by fuel-doping, you will have to get the right kind of screwdriver for the hi-lo mixture needles and play around with them until you get it running.
Also might have to work on the little 'box carb', which I personally hate to do.
I use Marvel Mystery Oil and Sta-Bil in my mixes which has been successful in preventing gummed-up carbs.

My reason for putting the fuel into the spark plug hole is to bypass much of the effect of the reed valve and the crankcase seal. Those play a vital role in getting the fuel/air mix into the cylinder. With fuel in the cylinder, and spark, the only thing needed is for the fuel/air mix to fall into the proper range for spark ignition.