The 1-2 shift happens almost as soon as the vehicle starts moving. Are you sure it's actually in 1st.? Here's what's happening in each gear:
1st.: Both bands applied, both clutches released. Both planetary units in reduction.
2nd.: Front band released, rear band applied. Front clutch applied. Rear clutch released. Front planetary unit in direct drive, rear planetary in reduction.
3rd.: Front band applied, rear band released. Rear clutch applied, front clutch released. Front planetary in reduction, rear planetary in direct drive.
4th.: Both bands released, both clutches applied. Both planetaries in direct drive. Almost 100% lockup of fluid coupling in all gears, no torque multiplication in the fluid coupling on breakaway.
To check for 1st gear band slippage, lock the brakes and go to full throttle. The engine should stall at 1900 RPM or less and will not accelerate further. 10 seconds maximum for this test, as it heats up the fluid in a hurry.
Transmissions with a torque converter instead of a fluid drive, like a Powerglide have almost a 2:1 torque multiplication before the transmission input shaft starts to move on breakaway, but the converter has a built-in 10% slippage which cannot be overcome without putting a mechanical clutch inside the converter. The first converter clutch was used in the 1949 Studebaker automatic trans, BTW.
I can scan and forward the full road test sequence for all gears if you want it- - - -send me your email address by PM.
Jerry