Would low pump oil cause the engine to not start?

Good question. Many things to eliminate. You might want to have a mechanic narrow this down with a diagnosis. Otherwise, here are possible causes:

Fuel pressure regulator: If the fuel pressure regulator is faulty, it can cause the engine to start and then stall immediately. You may want to check the fuel pressure regulator to see if it's working properly.

Fuel pump relay: A faulty fuel pump relay can cause the engine to start and then stall immediately. You may want to check the fuel pump relay to see if it's working properly.

Crankshaft position sensor: If the crankshaft position sensor is faulty, it can cause the engine to start and then stall immediately. You may want to check the crankshaft position sensor to see if it's working properly.

Ignition switch: A faulty ignition switch can cause the engine to start and then stall immediately. You may want to check the ignition switch to see if it's working properly.

Battery: If the battery is weak or dead, it can cause the engine to start and then stall immediately. You may want to check the battery to see if it's working properly.

Fuel filter: A clogged fuel filter can cause the engine to start and then stall immediately. You mentioned that you already changed the fuel filter, but it's possible that there's still an issue with it.

Vacuum leak: A vacuum leak can cause the engine to start and then stall immediately. You may want to check for any vacuum leaks in your truck.

Based on the information you've provided, there are a few possibilities for what could be causing the issues with your Toro Dingo:

Engine damage: Running the engine with very low oil can cause serious damage to the engine, including wear on bearings and pistons. This can result in a loss of power and difficulty starting. If the engine is damaged, it may need to be rebuilt or replaced.

Hydraulic system issues: The low hydraulic oil level and small hose leak could be causing issues with the performance of the trencher attachment and other hydraulic functions on the machine. It's possible that the hydraulic pump is not getting enough oil, which could cause a loss of power.

Fuel system issues: If the machine was running on low fuel, it's possible that debris from the fuel tank could have entered the fuel lines and clogged the fuel filter or injectors. This could cause the machine to stall or run poorly.

Given the symptoms you've described, it's difficult to determine the exact cause of the problem without further diagnostic testing. If you're not able to perform a compression check or other diagnostic tests yourself, it may be best to take the machine to a qualified mechanic who can perform a thorough inspection and provide an accurate diagnosis. They can also perform any necessary repairs to get the machine running smoothly again.

check oil level low or no oil causes no start so does --your oil sender may have failed --oil sender also has a screen filter which causes low or no pressure =oil pump problem ==the truck wont start or may start and shut off immediately

The oil pressure warning light is designed to illuminate any time the oil pressure is too low (below a pre-set engineering-specification). Low oil pressure can be caused by an oil level that is too low, a faulty oil pump or worn out engine bearings. The light could also potentially illuminate if the engine idle speed is excessively low (near stalling condition) due to the slow rate of pump rotation. There is also the possibility that a failure in the oil pressure warning circuit is causing the light to illuminate inappropriately; this could be the result of a failed oil pressure sensor or other wiring issue. Because the other symptom present is an engine stall (shuts off) condition, I'd recommend inspecting for a mechanical issue first. Ensure the oil level is correct, then attempt to turn the engine over by hand using a large ratchet on the center crankshaft pulley bolt; if the engine can be rotated it was not stalled out by a seized condition (which could be caused by a lack of oil pressure). If the engine runs but idles low, I'd suggest raising the RPM to see if the light goes away and prevents the stalling-out. If everything appears OK with a raised idle then the idle control system should be inspected. On the other hand if the light remains on, a mechanical oil pressure gauge should be installed to the oil pressure test port (near the oil filter) to confirm whether or not the oil pump is producing adequate oil pressure. You can read more here: https://www.yourmechanic.com/article/how-do-you-know-if-the-oil-pressure-gauge-is-bad

First thing I would check is the coolant and engine oil to make sure they are full. If the coolant is low it could have been overheating the engine. This could cause the engine to bind and stall if it gets hot enough. If it was shut off in time it might start and run fine until it gets too hot again. Also if the oil is too low it can cause the hydraulic lifters in the engine to not work properly and they will make a ticking sound. worst case if ran with low oil long enough it could cause bearing failure and create a knocking sound.

hot or cold engine , or both.?
the oil pressure will be in direct ratio to engine rpm. slow low, fast high
due to the oil pump connection to engine crankshaft.

stalls.: can be caused by 50 things, or just 4 in physics.
the EGR valve (if you have one, no engine stated)
can stick open and stall any engine, and in fact LOVES to. clean it.
1: list 12vdc to EFI. (spark and fuel brain) dash lights dim?
2: lost compression hot, ? compression tests.
3: lost spark, do spark tests. and timing, checks.
4: bad fueling, too much if floods, and misfires and stalls.
too little fuel, it starves and dies.

the 1 free test, is can you save the stall with a fast right foot.

we do the tests. avoiding those 50 guesses....
each tests are simple and the tools dirt cheap .

Don't run the engine. Low oil pressure will cause damage to moving parts. Have it towed or pulled to a shop where true oil pressure can be checked with a gauge. Could be a worn oil pump, but lots of possibilities (like oil passage blockage) other than the oil pump.

To start with, why on earth would an engine with re-used bearings, oil pump and cam need a "break-in" in the first place?

Then, it deserves mention that the number 1 cause of low oil pressure in a small block chevy engine is wear in the cam and/or cam bearings. The second highest cause is worn crankshaft main and rod bearings and the third highest cause is an oil pump that has too much internal clearance or an oil pump pick-up screen that is clogged with debris from shady repair work.

Sounds to me like you problem is probably related to the fact that the engine has not been "built", but rather, assembled with the same old worn out parts that most likely caused the need for it to be "built" in the first place.

LOW OIL PRESSURE WILL CAUSE OIL PRESSURE SWITCH OR SENDING UNIT TO DISABLE FUEL PUMP.CHECK FOR OIL PRESSURE.REMOVE OIL PRESSURE SENDING UNIT SCREW IN OIL PRESSURE GAUGE TESTER INTO BLOCK WHERE OIL PRESSURE SENDING UNIT GOES TURN ENGINE OVER CHECK FOR OIL PRESSURE SHOULD BE 18 PSI @ 2000 RPM. BESURE TO WRAP TEFLON PLUMBERS TAPE AROUND THREADS TO THE OIL GAUGE PRESSURE TESTER OIL WILL SPRAY EVERY WHERE.IF YOU ARE GETTING NO OIL PRESSURE.YOUR OIL PUMP FAULTY.YOUR ENGINE CRANKSHAFT BEARINGS WORN OUT.WORN DAMAGED CAMSHAFT OIL PUMP DRIVE GEAR OR OIL PUMP DRIVE ROD DAMAGED OR BROKEN. IF OIL PRESSURE OKAY OIL PRESSURE SENDING UNIT IS BAD.

This sounds like overheating. These small generators don't have overheating protection, but if a low oil pressure or low oil level is present it may be the reason for stopping.

Check the oil level in the starting conditions and again when it stops. It may become under the "stop" level and after some time the precipitated oil has reached the "start" level. The same may be with oil viscosity and oil pressure.

Try to add some oil or change the oil with bigger viscosity.