Remove the air cleaner assembly & look at the butterfly -- there will be a shaft running thru the center of it -- on one end or the other, there should be a linkage of some sort. This will lead to wherever the lever is to activate the choke. Try moving the butterfly with your finger -- if you can see straight down the carburetor bore, it's open -- choke off. I know of no engine that does not have a choke or enrichener system.
A 2-stroke should start in no more than 3 pulls. If not, then either the fuel isn't getting to the carb ( which is what it sounds like ) or there is a weak spark -- or low compression......unlikely on a new machine, but possible considering the quality of some items I've purchased at big box stores. Could be as simple as a pinhole in the primer system. If just a tiny bit of air gets in there, it won't do it's job -- which is to fill the carburetor with fuel. Another factor could be the fuel/oil mixture. Leaner is better, contrary to popular belief (within reason). I mix everything at 50 - 55:1 with a good synthetic oil. They run soooo much better! Also, if there is an adjustment on the carb ( usually restricted with a cap ), it helps starting to turn them out about 1/4 to 1/2 turn. They set them up so lean that they barely run, all in the name of clean air...
I'll take a 2-stroke any day over a 4-stroke -- they are lighter (important for something you have to carry around), more powerful for a given size, & easier to start (when everything is working properly).
Well I just typed all this & it looks like you found it!