Why do we have to put off every issue with a semi-fitting explanation as being normal. Are we lying to ourselves? No, that sound is not normal. It's a noise and something is wrong. Just because it's inconvenient to deal with it, it's still a problem.
We're not in his vehicle, so we can't hear what he's hearing, but from what the poster stated his noise coincides with the normal ABS Diagnosis self check.
1) the noise happens when the vehicle is first started
2) the noise happens as the vehicle first moves
3) can be felt in the pedals
That matches the ABS self check noice:
When AdvanceTrac with RSC performs a normal system self-check,
some drivers may notice a slight movement of the brake, and/or a
rumble, grunting, or grinding noise after startup and when driving off.
An ABS self-check noise is normal and it should make a noise when its performing the self-check. The system checks the sensors on each wheel as they rotate, and then activates the ABS pump which groans and grunts and shakes the pedal. If you have ever activated the ABS system during braking, the sounds and vibrations are similar but to a different scale.
The Explorer has a much more sophisticated ABS/ESC/RSC/Curve Control/Trailer Sway system than most vehicles and probably makes more checks than other vehicles.
All vehicles with ABS do a self check.
For example:
NISSAN VEHICLES:
Date: June 10, 2010
ABS SELF CHECK NOISE
APPLIED VEHICLES: All Nissan Vehicles with ABS or ABS/VDC
SERVICE INFORMATION
If you identify:
^ Clicking, knocking, clunking, buzzing, or thumping noise coming from the engine compartment area; and
^ The noise occurs only once during the first few seconds of driving at approximately 16 MPH; and
^ The noise occurs only once per ignition cycle (ignition OFF > ON) and does not occur again until the ignition is cycled.
NOTE:
The noise may be louder after the vehicle has not been operated for a prolonged period of time.
The above condition is normal and does not need repair.
Each time the ignition is turned on and the vehicle is driven at about 16 mph, the ABS/VDC system performs a "Self-Check" to confirm components of the ABS/VDC system are operating correctly.
This "Self-Check" function creates the noise described above.
If the brakes are being applied when the "Self-Check" occurs, a vibration may be felt in the brake pedal and an increased level of noise may be noticed.
NOTE: ^ Refer customers to the Owners Manual, Section 5, Starting and driving, Brake system on the Anti-Lock Braking System (ABS). The "Self-test feature" section provides additional explanation.
^ The speeds described above refer specifically to Versa, Sentra, Altima, and Maxima. However, any vehicle fitted with ABS or ABS/VDC will have a "Self-Check" which is triggered in similar circumstances.
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Manufacturer: HONDA
Subject: ABS GRUNTS WHEN DOING A SELF- CHECK
Vehicle Involved: Honda Accord, Civic, Pilot, CR-V
Repair Procedure: If the owner of a vehicle equipped with a “compact” integrated ABS system complains of hearing a grunt or groan when backing or moving the vehicle forward after it’s been sitting idle, it may be the ABS system doing a self-check. An integrated system is composed of a modulator valve body, a pump, and an accumulator all rolled into one assembly, it is designed to self-check when the vehicle is moved forward or backward after sitting. So the grunt sound is normal; it does not indicate a problem with the ABS system.
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Toyota:
http://www.tundratalk.net/forums/tundra-general-discussion/85340-vcs-abs-self-check-noise-whatever-thay-call.html
