transmission

Transmission engaging when cold:
200K on the clock, 1997 E-150-Clubwagon. Transmissionlevel checked when running,
it is okay, no leak.
When it is cold the transmission is not engaging, only reverse.  I warm the car up By
backing up a little ramp, stop, shift into 1 gear,  let the car role forward while trying to
get the transmiiosn engage by pressing gently the accelerator. I do this three times
and it engages. Once the van is warm it shifts okay, here and there it hesitates to
automatically shift down form 3 to second gear.
What I discovered today: WHen car is cold, in Parking position, I push the accelerator
around seven times to rev the engine up. let go back to idle , I shift into 1 gear and the
transmission engages. Any advice?
The car runs strong engine wise, is it worth to rebuild the tranny or are there other
things, like filter change or fluid change,etc that will resolve the issue. Winter is coming
and the time for riding my motorcycle will be limited. thank you for your responds.