"New" is a problem in this case. New \6 fuel pumps tend to be much poorer quality than we used to be able to get. They no longer have the arm follower spring—which is what kept the pump's lever arm in contact with the camshaft even when the mainspring was compressed. Without the follower spring, when the mainspring's compressed, the lever arm is free to flop up and down, and in that condition it can easily make a click/tick/rattle when the cam lobe smacks it.
If you go too far the other direction, old fuel pumps pose risks as well—rubber doesn't react well to age, and some of it doesn't react well to alcohol in the fuel—but I had consistently fine results buying and using NOS AC № 6972 fuel pumps. Cheap and easy on eBay, such as this and this.
OP: to check if this is what's causing your noise, unbolt the fuel pump and pull it away from the block. Start the engine; if it was running recently, the fuel in the carb bowl should be enough to run it long enough for you to hear if the noise has gone.