The version of OpenSSL expected differs by the operating system version. So depending which binary you downloaded, it may require OpenSSL 1.1 or one of the newer versions.
Some internal folks noted that Posit doesn't support Amazon Linux 2023, as there are other packages (notably, pandoc) that aren't part of the image. So even if you get OpenSSL installed, you may still have issues. If you use a newer version of Ubuntu (22 for instance), it will link against OpenSSL 3.
Best,
Randy