Can I bypass the cutoff switch?

There is no cutoff switch on that vehicle. What is the issue you are having? Will not start? Antitheft light on? Starts but won't stay running? Is the check engine light on?

Was this a problem with the old engine or only after the replacement? What year is the new engine? The first thing I would check is if the fuel pump is getting power. The Green wire is battery power and the Black wire is ground. The green wire gets power from the relay which is turned on by the PCM. If you connect a test light to the pumps power connection it should light when you turn the key to the start position. If there is no power to the pump then we can test at the pump relay using a test light connected to ground, with the relay removed there should be two pins in the socket with power. One will have power full time, the other with the key on. If you find those the other two contacts are the control ground and power out to the pump. If you connect the test light to battery power and probe those two pins, it should light on one pin if the wiring to the pump is okay and on the other pin if the key is turned to the start position. The relay should have markings on it showing the coil side and the switch side. If you have power to the pump but no fuel pressure at the engine then it could be a blocked line or the pump isn't moving fuel.
A quick way to check the system would be to go to the data link connection under the hood on the left side, find pin 13 which is a green power feed to the fuel pump and using a fused test lead apply battery power to that pin, that should send power to the pump and let you test easier. That pin should also get power from the pump relay with the switch in the start position as the PCM turns the relay on.

Okay, if you put in a jumper and still didn't get fuel to the engine then either the pump itself is bad or there is an internal leak in the pump to tank fittings.

I would put a fuel pressure gauge on it and see what you have for pressure. You need an inline adapter for that car but then when you apply power to the pump you should have 46-50 psi. Then when you remove power that pressure should hold for about 5 minutes. If the pressure doesn't get to 46 or once power is removed it drops real fast then it's likely a leak.
When the pump was replaced was it the pump only or the entire pump module? I have seen the hose highlighted in the second image fail before, then you get low or no pressure at the engine.

If you bypass power to the pump does it come on then? If yes then the issue is in the control side of the relay which means an issue with the PCM not telling it to close. You said that the engine will start on spray but then won't stay running, if you jump power to the pump does it stay running then?

There are multiple items that have to work properly for the PCM to turn on the pump. If you jumper power so that the pump comes on did the engine run? If yes then the next step would be to use a dealer level scan tool to look at the live data and the inputs to the PCM that tell it that the engine is cranking and see if it is sending out the control signal to the relay on pin 20 of connector A, if the ground there is operating as it should then the wiring between the relay and the PCM has a fault. If the ground signal isn't there but all of the inputs to the PCM are OK then it may be the PCM itself has failed and will need to be replaced. It could also be security related as that shuts off the fuel if it doesn't get the proper inputs but to see those you need the scan tool as well. If the inputs to the PCM show that it is correct and it still doesn't turn the pump relay on then you would need to replace it and program the new one to work in your vehicle.