2002 Chevrolet Suburban - Odd noise

when I start off, at about 10 mph I hear a sound kind of like thumbing a deck of cards. If I take my foot off of the gas pedal, it stops. Once I get to about 25 mph, I don’t hear it anymore.

I’m going to give you two wildly different possibilities…

If you Subby is equipped with 4 wheel drive or any variation, AWD, push button selectable 4WD, AWD, 4WLo, I’d have the transfer case checked. You may have a leak that is creating a noise OR the transfer case chain is worn out and rattling against the case.

Or, one of the blend door actuators in the heat and AC system under your dashboard is failing and causing a click-click-click noise. Eventually the computer gives up when it can’t read the actuator and it stops. Common problem on these trucks.

Yes!
This is indeed a very common problem with those vehicles.

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The other possibility is that you have a U-joint that is beginning to fail.

Yosemite

If the sound is from the rear it may be universal joint noise, if so they have failed and must be replaced.