How to use gpg --gen-key in a script?

OpenSSL does not support OpenPGP, so you can't use it for key generation. Anyway, GnuPG is rather easy to script using --with-colons together with --batch. For most operations, using GPGME is the way to go, at least for high-level programming languages where libraries exist to interface GnuPG through it without having to parse the output on your own.

Also scripted key generation is possible: you're looking for unattended key generation, which is well possible. In the end it boils down to storing a description on how to generate the keys in a file, and running gpg --batch --genkey [filename].

The documentation linked above hosts following example on unattended key generation:

$ cat >foo <<EOF
     %echo Generating a basic OpenPGP key
     Key-Type: DSA
     Key-Length: 1024
     Subkey-Type: ELG-E
     Subkey-Length: 1024
     Name-Real: Joe Tester
     Name-Comment: with stupid passphrase
     Name-Email: joe@foo.bar
     Expire-Date: 0
     Passphrase: abc
     %pubring foo.pub
     %secring foo.sec
     # Do a commit here, so that we can later print "done" :-)
     %commit
     %echo done
EOF
$ gpg2 --batch --gen-key foo
 [...]
$ gpg2 --no-default-keyring --secret-keyring ./foo.sec \
       --keyring ./foo.pub --list-secret-keys
/home/wk/work/gnupg-stable/scratch/foo.sec
------------------------------------------
sec  1024D/915A878D 2000-03-09 Joe Tester (with stupid passphrase) <joe@foo.bar>
ssb  1024g/8F70E2C0 2000-03-09

$ gpg --quick-gen-key --batch --passphrase '...' a@gmail.com

From what I can see --quick-gen-key is a better choice for scripts:

4.5.3 The quick key manipulation interface

Recent versions of GnuPG have an interface to manipulate keys without using the interactive command --edit-key. This interface was added mainly for the benefit of GPGME (please consider using GPGME, see the manual subsection “Programmatic use of GnuPG”).

https://www.gnupg.org/documentation/manuals/gnupg/The-quick-key-manipulation-interface.html

4.5 Unattended Usage

gpg is often used as a backend engine by other software. To help with this a machine interface has been defined to have an unambiguous way to do this. The options --status-fd and --batch are almost always required for this.

• Programmatic use of GnuPG: Programmatic use of GnuPG
• Ephemeral home directories: Ephemeral home directories
• The quick key manipulation interface: The quick key manipulation interface

https://www.gnupg.org/documentation/manuals/gnupg/Unattended-Usage-of-GPG.html

--batch makes it not ask questions (except for a passphrase):

--batch
--no-batch
Use batch mode. Never ask, do not allow interactive commands.

https://man.archlinux.org/man/core/gnupg/gpg.1.en

Or a bigger example.