Thank you for the additional information.
With the information you provided, it is indicating we need to do a compression test and see exactly what we are getting on both cylinders. Why I request that is based on your description of the fuel apparently moving through the carb but no start. That narrows down the highest probability items to either a mechanical problem that is preventing the engine from creating the vacuum needed to draw fuel in, or, a restriction or assembly issue with the carb.
Out if curiosity, which fitting on the fuel pump do you have the fuel in on?
That notwithstanding, my gut instinct is it sounds like the carb is not correctly assembled.I am not attempting to criticize you here, but respond honestly to your information and get you up and running ASAP. Sometimes, in the process of doing that, it is necessary to question a procedure, so please don't take it personally. I am asking you to do exactly what I would be doing if you brought your ski to me to have a look at it. If it is truly drawing fuel from the tank into the carb, engine vacuum should pull the fuel from the fuel chamber into the engine. If it is coming in and returning......... we need to figure out what is preventing the engine from getting fuel.
This is a curious set of symptoms you are providing. Based solely on your description, it would be reasonable to expect the engine to run. It also sounds like the fuel pump is working because it is drawing fuel from the tank to the carb. My only thought there would be testing how quickly it fills the fuel lines by emptying the line from the filter to the carb, and see how long ti takes to fill back up. Do you know where you set your fuel screws at?