How can I prove to S.S office that I returned on time without the stamp of US customs on my passport? [closed]

One of the options would be retaining the boarding passes. If you use Global Entry, make a picture of that receipt that comes out of the machine, before you hand it to the customs.

According to the link helpfully supplied by Dennis in a comment, the following are required as evidence:

Obtain the following information when continuous presence must be proven:

1. Individual's statement

A signed statement from the claimant giving the date he/she entered the U.S., the place at which he/she stayed in this country during the first full month, and affirming that he/she did not go outside the U.S. at any time during such a month; and

2. Supporting evidence

Any evidence which establishes the claimant's date of entry into the U.S.; such as:

a. A copy of the return plane ticket, a passport showing the date of entry and date of departure, or similar evidence which establishes the date of entry; or

b. A signed statement from one or more U.S. residents having knowledge of the claimant's presence in the U.S. to corroborate his/her presence during the 30 days in question. A statement from the person who furnished the recipient lodging throughout the month in question is preferable. Statements from a member of the clergy, neighbors, or anyone else likely to have knowledge of the claimant's presence in this country are also acceptable. Persons executing corroborative statements must give their addresses and must indicate the basis for their knowledge.

NOTE: The date of departure is material for redeterminations to determine the duration of an absence. Use the evidence above to obtain such date.

You could also try showing credit card, bank card, or other receipts for transactions in the US after your arrival.