Note the uploaded photo is a larger, better quality image than the newspaper photo.
A search for renewal was done at copyright.gov for the newspaper's title and for Associated Press in 1957. There were no listings for Associated Press for 1957 and no renewals for Corpus Christi Caller-Times; only more recent original registrations. There's no evidence of continuing copyright.
Note that it may still be copyrighted in jurisdictions that do not apply the rule of the shorter term for US works (depending on the date of the author's death), such as Canada (70 years p.m.a.), Mainland China (50 years p.m.a., not Hong Kong or Macao), Germany (70 years p.m.a.), Mexico (100 years p.m.a.), Switzerland (70 years p.m.a.), and other countries with individual treaties.
{{Information |Description=Photo of Humphrey Bogart and his family in April 1956. From left: son Stephen, wife Lauren Bacall, daughter Leslie and Bogart. |Source=[https://www.newspapers.com/clip/5897389/humphrey_bogart_and_family_1956/ Corpus Christi C...