Sure, it can do it in one of three ways.
First, if the engine is revving up but you are not going anywhere fast, then its slipping and causing the problem.
But, you almost certainly would have realized that, so I'm guessing that the engine is bogging down.
In that case, we are left with two possibilites.
First, realize that in an automatic tranny, you do not actually shift gears. All the gears are engaged all the time.
Instead it applies clutches and/or brake bands to apply the different gears into and out of the drive line.
If one brake or clutch fails to release all the way, then you are basically in two gears at the same time.
Which will suck the heck out of the power. When it shifts out of first, then the problem goes away and the truck runs normally.
Since for it to move in that condition at all, one or the other of the clutches or brakes has to slip.
Pull the dipstick and look for burnt fluid or a bad odor.
The other way concerns the torque converter. In a way that would take too long to explain, it actually multiplies torque up to the stall speed.
You get more power at startup than you would if you just had a clutch in there.
Stall speed is not the rpm that the converter stalls the engine, its the speed when it "stalls" and becomes a direct drive.
If it develops a problem and quits multiplying torque, the engine will feel underpowered at low rpms.
However, low power off the line is way more often due to a timing, vacuum leak, or an EGR valve malfunction, or other engine problems than transmission.
Unless you have other reasons to suspect the transmission, strange noises, rpm not matching speed, then all I would do at this point is pull the dipstick and check the fluid.
If its nice and pink, concentrate on the engine first.
