The use of the engine number as the VIN was common through '55. It varied by state but I believe most states used the engine number with a few using the Unit Serial Number or other identifier.
Your issue is the main reason this question gets asked a LOT here. Someone along the line changed the engine and never retitled the vehicle so now they want to sell, or buy a vehicle and the number on the title is no where to be found on the vehicle.
The best answer every time is to contact the state licensing authority in your state and ask them what their preferred method is to change the title. All states have run into this issue a lot and all states have a way of solving the problem. My advise would be to contact the state office, not the local tag office. While some local workers may know the answer, most are bottom wage folks who've never dealt with the issue. Good luck with it.
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