The below from the manual looks to be what you should attempt to do. I'd have the arduino send 90 deg or 1500us signal to the ESC, connect the battery pack to the ESC, and then listen for the beeps. You probably need to follow the manual to set up the throttle range prior to the normal startup.
Normal Startup Procedure
Move throttle stick to the neutral position
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Switch on the transmitter
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Connect battery pack to ESC
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System detects the
neutral throttle signal, makes a long “beep-” sound
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System detects battery voltage and makes several short “beep-” sounds, which
denotes the number of battery cells
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when self-test is finished
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“
F 1 2 3
”
tone should be emitted
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ready for start.
Setting Throttle Range (Throttle range should be setup when a new transmitter is being used)