I'm 37 weeks and just packed a couple days ago
You can pack in bits and pieces but make sure all is packed by 36 weeks so that you're not under pressure.
My midwife recommended having the hospital bag packed and the car seat installed by week 36 just in case baby comes early. We packed the bag a little bit at a time over a few weeks and thankfully had it all done when I was unexpectedly induced at my "routine" 39 week appointment. Last thing you want is to be dealing with packing last minute while you're in labor