Brief rumbling/grinding noise when I first start moving

When I first take off from a traffic light, there is a rough rumbling/grinding noise which quickly stops. I can hear it and feel it in the steering wheel. It's strong enough that a passenger can feel it. It's almost like you're driving over something very rough, like bad asphalt. It only lasts a few seconds then rides smooth. Happens every time.

If I start off in 4WD or in reverse, I don't hear/feel it.

It feels like it's something in the transmission/transfer case/differential, or possibly wheel bearings. I'm more of an engine guy, not too much experience with the drivetrain south the flywheel....

It's a 2006 Tacoma 4WD with 160k miles and a 4" lift. I just bought it used and didn't notice it during the test drive. I'm not sure but I think it's getting worse :crying:

 

Not sure you are having the same problem I did with my 2012 sport. I have the 4.0L. When reversing if I let the engine bog down, I'll hear this grinding noise. At first I was worried about it. I realized it didn't start till after I changed the air filter. I found it to be the air intake tube in the fender rattling around when the engine shakes. Not sure what you have, but mine was an easy fix. Didn't try it in 4 wheel. Sometimes it would happen when taking off in first (6 speed man.). I felt it in my steering wheel, floor, ears. My passenger could also hear it, not feel it.