First, export the relevant environment variables e.g. S3_ACCESS_KEY, S3_SECRET_KEY, S3_REGION

To upload a file foo.gz to path /backups/db/foo.gz , use the following command.

curl --progress-bar \
          -X PUT \
          --user "${S3_ACCESS_KEY}":"${S3_SECRET_KEY}" \
          --aws-sigv4 "aws:amz:${S3_REGION}:s3" \
          --upload-file foo.gz \
          "https://${S3_BUCKET}.s3.${S3_REGION}.amazonaws.com/backups/db/foo.gz"

Note that you would a recent version (Feb 2021) of curl that natively supports aws v4 signature authentication (https://curl.se/docs/manpage.html#–aws-sigv4). for older version of curl, you may to send special headers (idk)!