If the car was sold in the last week, you wouldn't see this in the public database yet.
Assuming the speaker knows that when a car is sold it doesn't turn up in the database until two weeks later, there are two contexts in which it can be uttered:
(1) the actual world
The context is that the speaker is talking about the actual world.
In this case, the past tense verb was, therefore, denotes the past time (last week) in the actual world, and you would normally have won't instead of wouldn't as follows:
If the car was sold in the last week, you won't see this in the public database yet.
But wouldn't isn't impossible, because it can convey some uncertainty that the speaker is not 100% sure about the assumption presented at the outset, or merely because the speaker doesn't want to sound too direct.
(2) a hypothetical/counterfactual world
The context is that the speaker is talking about a hypothetical world, and possibly even a counterfactual world.
In this case, the past tense verb wouldn't, therefore, denotes a hypothetical or even counterfactual world, and you would normally have had been instead of was as follows:
If the car had been sold in the last week, you wouldn't see this in the public database yet.
But was isn't impossible, because in informal speech the simple past tense in the if-clause can often represent a hypothetical/counterfactual world in the past time.