In some dealerships, as high as 40% of customers get rejected for finance, so making an application the final step in the sales journey makes little sense.
It is a waste of time and resources for everyone. So move it to the front end of the process. This sounds as though it might spoil the flow of the sales journey but it is actually quite logical.
Talk to the customer about their budget and the kind of price range in which they will be looking, and carry out a sample finance application through a finance pre-qualifier to see whether their credit is likely to be acceptable.