You may not sue the post office for failing to deliver mail to you, or failing to deliver mail you sent to someone else.
The Federal Tort Claims Act allows for a claim to be brought against the United States government for personal injury, death, or loss of property, resulting from the negligent or wrongful act or omission of any employee of the Government, while acting within the scope of his office or employment. See 28 U.S. Code § 2679.
You can sue the Post Office if you are negligently struck by a post office truck. You can sue the Post Office if you slip and fall in a Post Office building due to a hazardous condition. You can sue the United States Government if a government employee negligently causes you to be injured.
However, the Federal Tort Claims Act specifically states that you cannot sue the United States Government, or the U.S. Postal Service for “Any claim arising out of the loss, miscarriage, or negligent transmission of letters or postal matter.” See 28 U.S. Code § 2680.
Accordingly, you cannot the United States Postal Service for failing to deliver mail. At best, if you sent mail or a package via the Post Office, and purchased insurance, you can make a claim for the insured value, but nothing else.