Engine starts once and stalls, will not restart

Sounds like one of two main issues. First, if the engine was running fine but now starts and stalls as the idle comes down, it may have a fuel issue.

The other is a vacuum leak.

So let's start with a fuel issue. We want to start the engine and when it stalls, try to spray some starter fluid in the carb and try to start it.

If it starts then we have a fuel delivery issue so we are going to want to check and make sure the pump can deliver pressure. You do this by removing it and operating the arm and see if the diagram pushes air out the nipple on the bottom of it.

The way this works is the arm shown in the picture below rides on a cam lobe and as it spins it moves this arm up and down and that creates the fuel pressure needed to feed the carb.

If it does not start then I suspect it is due to it being flooded. Try hold your foot to the floor and crank the engine to see if it fires. This will open the throttle blades wide open and let in more air to try and compensate for the added fuel. If this is the case, we will need to pull the plugs and see what they look like as they could be fouled at this point.

Lastly we need to search for a vacuum leak and see if we have too much air coming in on the engine side of the carb which the carb would not be able to adjust for that.

https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge

Let's run through this info and go from there. If we can rule out a fuel issue then we can move onto spark but this does not sound like a spark issue.