5.7 votec chev avlanche 2004 . no oil pressure when started, when hit gas petal hard 3 or 4 times ,pressure comes right up. runs great after that

check the heatshield that runs over the exhaust system they have a habit of coming lose a self tapping screw normaly fixes it

Determining what caused sudden slack in valves would be of concern to me, as in perhaps, changed oil brand, grade or filter incorrect?
Most small block chevy's have adjustable rocker arms. Is that not the case with yours?

install pressure gauge and watch when key is turned off to see if pressure drops to zero if so bad drain back valve in fuel pump replace it or deal with it or could be cheap aftermarket pump and has hard time building unnecessary pressure to open poppet valves between before fuel injectors

You need to have the oil pressure checked with a manual oil pressure gauge you may have a bad sending unit. If the you oil pressure is the same with the manual gauge then you have a oil pressure problem.

No ressting to do. You need to remove all air from the fuel lines. Running out of gas in any fuel injected vehicle is a big no no for it is so expensive to get back running right. Add 5 gallons of fuel to get good priming pressure first of all
Turn the ignition key on for 5 secondes and turn it off for ten secocds. Do this step 5 time to bring up fuel pressure to the engine
Next try and start it
If it does not start release the air pressurized in the fuel line at the fuel rail above the engine. It looks like a tire air fill valve. Use a rag to catch the gas that spews out as you bleed the air out
Now turn the igition key on and off again for 5 times as stated above and proceed to start the engine once more
Good luck

it is happen when the fuel pressure detect thev insufficient fuel pressures, turn off engine while filling.

the oil light is coming on due to sensed low engine oil pressure, this is not a level issue unless u are about 3 quarts low, oil pressure indicators don't leave any computer codes, so who ever told u that is wrong, u need to test the oil pressure with a mechanical gage when the oil light is on, until U need to confirm that u don't have a real pressure issue here or you can burn out the engine bearings, if the pressure checks ok then rplace the oil pressure light sending unit in the engine.

that has a votec engine in it the fuel pressure is droping at knight and it takes 60 psi before the injectors will fire most likely cause fuel pump ,leaking injector ,or a feul pressure regulator

it will say in your owners manual but i believe you turn your ignition key to the run position not the start. and pump the gas pedal 3 times with in 5 seconds

Yes, it is a mechanical oil pump. Just for peace of mind, you could have the oil pressure checked. A mechanic shop could do it real easy-you remove the oil pressure sensor or sending unit from the engine block and hook up a "mechanical oil pressure gauge", then run the engine with gauge attached and check pressure against the specs for your model- it is a specified pressure at a specified engine rpm. I f oil pressure is within specs, I can't imagine anything else about the pump that could cause that noise. It is a compact unit with a couple of heavy internal gears.

If your mechanic didn't think it was a bearing or rod either, you should be safe there. He would know the sound of a rod bearing or mechanical problem like that, and if it is different from your sound. Beyond that and the oil pump, I just don't have any ideas.
Hope you find it, good luck.