Hi Todd, some tractors will run without the fuel transfer pump but the tank needs to be completely full of fuel, the system primed, and the rest of the fuel system needs to be in good shape. But it's obviously not the ideal situation and I'm not sure if the tractor would develop full or even half power like that. So it's possible the previous owner put it back together just to get it running enough to put it back in the shed. You can pick up another transfer pump from any of the team on here like Wally and Jon and Hector, but if they don't have one, then you can check with Dana at Florin Tractor and search with the part # on machinerytrader.com
For a part like this, Cat is unlikely to be able to help you.
To prime, fill the fuel tank full, open the fuel tank valve which is indicated by the line across the valve stem being inline with the valve body/flow (vs. across it). Open the bleeder valve at the front of the fuel filter tower, and if you have a working transfer pump in place, you can start the pony, decompress the main engine, and use the pony to turn the main engine over which will turn the transfer pump. After a minute or two, fuel will issue from the front bleeder. Close that then open the bleeder on the side of the fuel filter tower. Once fuel issues from that, close it. Then open the bleeders on the injection pumps. Once fuel issues from those without bubbles, close them. To start, you can leave the pony turning the main over, verify your governor control is fully closed (over the detent) and that you have oil pressure. Then close the decompressor and turn the main for a few minutes at full pony throttle. Snap the main engine governor control open and the main will normally start. If it does, turn the fuel off to the pony and idle it down and let it run out of gasoline at idle. If it doesn't start but you were getting smoke (white and maybe a couple of puffs of black), then it was about to start so give it another go, running on compression / no governor for a couple minutes more then try again. If it still doesn't start and it does issue much smoke, then you may need to bleed some more. If none of that helps, come back here for more discussion.
For the pony, since it only takes a quart and it's not filtered, change it early and often. When you first start it from cold, keep it at a low idle until it's had a chance to splash-lubricate and warm up a bit. That will help with longevity.

Thanks Dan, I forgot that bit! : ) Todd, I picked up a rubber drainage cap from Home Depot that fits over the fuel tank neck exactly, and with the right size hose clamp, can easily hold 5psi. I drilled a hole and fitted a Schrader valve to it and set my compressor to 5psi. Makes bleeding a lot faster and you don't necessarily have to run the pony to prime it (although it's good to so you can verify with a start that it's all good)