There should be a shiny metal plate riveted to the seat support. The tractor's serial number only appears on that plate. It appears nowhere else on the tractor. Once that plate is removed, it's impossible to find the tractor's original serial number, unless the previous owners have kept all the paperwork back to the original purchase.
Every major casting has a date code like that on it. You definitely need to check several castings to get an accurate idea of the age of the tractor, because it's quite common for major castings to have been changed out during the tractor's lifespan due to wear or damage. For example, if there's one casting with a W code, and 10 others with a T code, then the tractor is more likely a 1950.