First new bike ever. Can't start it.

Are you kicking from TDC?

You're running premix? Fuel on, choke on?

30 seconds isn't much for a heat cycle as you shut it down cold.

I'd be surprised if a brand new keihin pwk was buggered but not impossible.

Make sure it doesn’t have a butt plug in it. 

You really wouldn't see fuel spraying the reeds unless you kicked hard enough to create a vacuum. There's no accelerator pump on 2 strokes so fuel doesn't squirt like 4 strokes. You should see the reed pedals kinda glossy with premix tho.

If anything remove the carb, drain the bowl and blow out the jets. You could pick up a new spark plug as well.

Not sure when you bought it but yamaha does warranty their bikes for 30 days. If its not something obvious or simple I'd probably be thinking about taking it back and letting the dealer figure it out on yamahas dime instead of tearing into it yourself

What does the plug look like and are you running a standard fuel ratio or something more rich on oil for break in?

And check the float if it’s set rt.  I know a rider that bought a new gas gas 125 then drove to a race. He couldn’t get it started & worked on it at night. It was the float. 

It does sound frustrating. No changes to the bike at all?  
Do you have someone to push you, or enough of a slope to try to bump start it?

I did have a fuel petcock on my 125  that I had to replace the first week I owned it ( brand new bike ), have you pulled the line off of the carburetor and checked that fuel was flowing with the valve open?

I’d check the float since you verified you’re getting fuel to the carb, take a peak at the jets while you’re in there. If everything checks out roll it up a good hill and give it a solid bumpstart. 

Before you strip the carb, drain the fuel & replace. Also check for spark.

Straight back to the dealer.

This... never trust the shit from the dealer.  Unless they are personal friends of yours and not idiots.  About 2-3 yrs ago I had a guy with a brand new bike fouling plugs and running like shit because of whatever some goon at the dealer put in it.

Just my humble opinion:

-beyond changing spark plug and fuel, do NOT disassemble anything. If a new plug or fuel doesn’t fix it, bring it back to the dealer. 
 

What in the wide world of sports is going on here!!!!!

New spark plug would be my number one, and only repair, because you shut it off so quickly. Don’t do that again.

If a new plug doesn’t fix it then you go straight back to the dealer and politely ask for help.

Just hold it wide open and kick. You semi fouled plug by not getting enough heat into it when you ran it the night before. 

No heat cycles...let it warm up, check for any leaks and let it rip. 

Its not the premix! Its like above said a semi foulded plug. The engine wasnt hot enough to burn the fule and premix off when you shut her down. I see it mostly when people jump on there bikes before their warmed up and stall them right off the bat. Most the times they refire every now and then they don't. Keep a few plugs on ya.

RTFM and follow that break in procedure.

Can't be selective following a manual...some manuals want you to pull the top end to check things too, de-glaze, etc....nobody does that. These bikes are hard broke in at the factory. Tried and true method for ring seating...these are nikasil coated, not some iron bore. 

Guys on here who debate about break in would throw up knowing what the factory workers do in Japan before they seal the crate on your brand new bike. 

Make sure to replace that piston in 15 hours since you RTFM

If it is anything like a diesel engine it goes from the assembly line to full throttle on a dyno. They might warm it up a little before hitting the throttle stop but only long enough to look for oil/coolant leaks.

A lot of people going from 4 strokes to 2 strokes don't understand what it takes to keep the smoker running.  It's a little trickier than hitting the button.  Not that the OP doesn't know what he's doing....i'm not implying that.  But....you need to keep revving the bike to keep it running.  Most smokers are set to die at idle......