From the first time I read a script or first watch a cut I start thinking about what sounds in the film I would like to record, so that I can prioritise those & start organising time & access. I simply don't believe in the 'I dont have time to record' line - I've worked on plenty of low & no budget projects and it is your choice how you spend your time. If you really want to record something then there is always the evenings or weekend (which are often the best time anyway!)
I can give a good example: many years ago I got called in to help on a film that was having trouble with the sound team. An important sonic character in the film was a particular V8 car - there was a chase sequence & it also crashed into a petrol station which caught fire & exploded. I checked out what had been edited, the impacts, fire & explosion were good but car was very underwhelming & I asked what recording had been done "Oh we havent had time to record anything" - I didnt say anything but I thought, really? What they meant was either they hadn't prioritised it... or maybe there was some kind of psychological barrier?
So guess what? In less than half an hour of phone calls I tracked down a car with the same engine, I explained to the owner we didnt have big budget but I could cover petrol & some beers - the guy was keen. I drove to a quiet street, rigged the mics for onboard recording, did half an hour of driving. I then hopped out & gave him a list of moves I needed - passbys various speeds, up & stop, take offs etc... An hour later we were done.
So in under 3 hours total I did what the sound team had been putting off for literally months . And the really fundamental part of this is & what you maybe need to consider: it is FAR EASIER to edit a scene when you have material specifically recorded for it, than trying to piece it together from a library. The end result has so much more character and because you recorded it you were there & remember all the funny interesting sounds that add character... Especially vehicles where action is specific to picture cuts etc...
Access to gear isn't an excuse any more either - that car recording story was back in the day when I only had a DAT recorder, a 416 and two dynamic mics.... Recording great specific unique material, even with a single mic is far better than nothing, and you learn a lot in the process
Sometimes I will have a go at cutting a scene or sequence of FX from my library, or do a first pass of ambiences from my library & then think: what elements would really benefit from new material.
But remember above all else, it is more about priorities than 'not having time'