What some people do it have the shop do the pre-purchase to determine major airworthiness issues. Then if the sale goes through, they complete the annual (which includes things like lubrication and adjusting some things). No reason to pay for those things if you are not going to buy it.
I bought my first plane over the summer. As I started looking, I applied for the loan. Made things faster once a plane was found, and helped the seller realize I was serious about buying. Found the plane, had a mechanic look over the logs, and based on the logs, made an offer. Although you can make an offer contingent on the log inspection and pre-buy, with the option to revise the offer.. If the offer was accepted, I placed deposit. After the first one, the deposit was already in escrow, so could be transferred very quickly.
Then had the pre-buy, and negotiated any issues. Once everything was good, contacted the loan company about the final price, and the escrow company, who did their thing. In my case, these last steps after the pre-buy too about 2 days.
I used Dorr Aviation for the loan. And Aero Space Reports for escrow and title services. Both were amazing.
And notice I talked about the deposit as if it was multiple times. It was. The first plane had some questionable things about the engine in the logs and the seller would not accept the revised offer. The second one would not ferry the airplane to a pre-buy and wanted it done on their field. The 3rd one, the owner backed out that day it was too be delivered to the pre-buy (address the seller backing out in the purchase agreement). The final one went smoothly, and about 10 days (over a holiday weekend) from first ad to completed sale.