Each time a race loads, 6 cars are swapped out in the used car dealership.
So, you can either check every time after a race, or, a quicker method, is to use the licence tests. Assuming you have at least two unlocked.
Simply load up B Licence and select the first test. On the pre-race screen select next licence, on the next licence select previous licence, and so on... once you have seen 5 loading bars there should be 30 different cars in the dealership.
As it is seemingly random, this does not guarantee there will be one with over 300,000km, you may have to try a few times before one appears.
Also, make sure you have enough credits available: the first I saw was over 46,000Cr.