Right now, nginx 1.13.x requires compiling against OpenSSL 1.1.1 or newer to get TLSv1.3 supported in browsers.
You need to compile the "draft-18" branch of OpenSSL as current browsers are on draft-18 (master is on draft-19).
You need to compile the "draft-18" branch of OpenSSL as current browsers are on draft-18 (master is on draft-19).
Building apache from source is not only very straightforward but a great way to maximimize httpd performance (all modules static, only include the modules you need). OpenSSL on the other hand, that's distro specific, and definitely more involved.
git clone https://github.com/openssl/openssl.git -b tls1.3-draft-18 openssl-1.1.1-tls1.3-draft-18