My 65's still got original tranny, put fluid/filter in it when it was apart...still runs great, shifts fine- except it does the same thing when cold...often clogged filter simply cant pull enough oil when cold/thick, but not this one...apparently the old pump seals are just starting to go and it takes time to prime up, and get any air out of the system...suggestion- if the thing still does it after changing filter, try this: after starting, let it idle at least a few seconds, then move selector from drive -reverse-drive-reverse quickly enough it wont actually pull at all or go into gear...this will dump enough fluid volume thru the valve body to fully prime the system at no pressure, and prevent slipping the clutches, rapidly destroying them...Ive noticed on the 65 it would feel like it was sluggish/slipping when first trying to move, and that worried me enough to think about it a bit...if you try it, I'm sure it will take all of about 3 seconds to get a feel for how fast to move the lever before car even tries to budge(clutches not even trying to engage yet) and if its like mine, after few cycles of the selector it goes solidly into gear, and dont slip at all when you pull out...first automatic shift is firmer also. Automatic tranny clutches dont like slippage...be it clutches or bands, they just cannot dissipate heat generated by slippage. Shifting valve body/partially actuating servos will flow enough oil to prime the pump faster, and allow any air that might get into system while sitting, to get pushed out rather than compressed, which severely softens the first couple shifts.
it's works for me anyways. think we've put about 2000 miles on it, and it had sat for 20 years. Dont really want to think about rebuilding it- old cruiso parts seem rather scarce...couldnt even get a pan gasket for mine, had to buy a roll and make one.