What you have is delayed ignition. It's being caused by the gas regulator. It is solvable, though.
Turn the gas tank valve OFF and disconnect the hose from the tank.
Wait 5 minutes and reconnect the hose to the tank.
Open the tank valve VERY, VERY SLOWLY (Slow motion, slow).
Once the valve is fully open, light 1 burner and turn it to HIGH. Did the burner light and does th eflame height look correct? If so, light the remaining burner the identical same way. Now, to both flame heights look correct? If so, you solved the problem. Remember to always open the tank valve Very, Very Slowly. And always light the burners with the Lid/Hood Open.
If the above did not solve the problem, you will need to replace the Hose/Regulator Assembly. Since your grill is brand new, the Hose/Regulator Assembly will be covered under Warranty. Have your Proof of Purchase handy and call Weber 1-800-446-1071. Also, if you haven't done so already, register your grill before calling http://help.weber.com/register/
even if you don't need a new Hose/Regulator Assembly.
Hope this helped you troubleshoot & solve the problem.