The only way to try to find the date is to remove the neck from the body. If the year is unreadable, it can also be written on the body under the pickguard or in the cavity in which the pickups are. With Fenders from before 1955 you cannot use the serial numbers to determine the exact year of construction.

How can I tell when my guitar was made?

Look for a date marker on the neck. There should be a date on the neck and a date on the body. If those two dates match up, thats probably the exact date your guitar was built.