Umm...maybe it's just a film and the charatcer had a certain look they wanted to manitain (familiarity for the viewers of the sequels) and so continuity was just glossed over?
Seriously....
However..in the spirit of this thread....he acquired
a fedora as a boy...jacket..whip..bag...etc. non of which would last too long due to bullet holes..abrasion on tank tracks...or being dragged along the ground by a truck..etc.
The hat and get up were "fashionable" and probably common place in the 30/40's...and so the "look" was maintained, through ease of availability, or even just personal tatse or superstition on Indy's part.
How many times do you find a perfect hat/coat etc? So why not buy identical ones again? Heck my GF buys shoes/clothes in every colour of a style she likes!!
Alternatively it was all the same kit that always came back into his hands before the next adventure required them and any damage was patched up with needle, thread and a splash of grail water...they don't make em like they used to!