RE: 70cc 3W engine with Tillotson carb 3s222b337.
A two cycle engine will run for a short burst with the carb removed and a squirt of gas in the crankcase. If it doesn't run when you spray gas in the carb, you're not putting enough gas in or you have other problems other than the carb.Ignition, plug, reeds would be where I would start looking.
Your carb could be simply dry, did you wet anything when assembled? If you can push the metering diaphragm down though the vent hole while flipping it over that might get it pumping. The pumps make 10-12 psi pressure while the pop off pressure is higher. When starting the vacuum in the crankcase pulls the diaphragm down while choking, with a dry chamber this isn't always possible since air is compressible.