Yes, you can adjust the harshness of the shift via the vacuum modulator on the transmission. Do a search. It has been discussed a lot.
Last, your hard shift is not from 1st to 2nd, but from 2nd to 3rd. You have a 4-speed transmission, but it starts in 2nd gear.
1992 and later 300E's start in 1st gear.
You can engage first gear start by moving your gear shift lever all the way down to 2, then up to 'D', or buy mashing the accelerator to the floor.
2001 E430, Bourdeaux Red, Oyster interior.
1973 280SE 4.5, 170,000 miles. 568 Signal Red, Black MB Tex. "The Red Baron".