Did you create and start a database using something like the following?
/usr/local/mysql/scripts/mysql_install_db --no-defaults --basedir=/usr/local/mysql --datadir=/path/to/database/dir
sudo /usr/local/mysql/bin/mysqld_safe --basedir=/usr/local/mysql --datadir=/path/to/database/dir --syslog --user=tc &
The socket is in the default location. It won't exist until the database is started. You can change the location in the config file:
tc@box:/usr/local/mysql/bin$ ./mysql --help
./mysql Ver 15.1 Distrib 10.3.13-MariaDB, for Linux (i686) using readline 5.1
Copyright (c) 2000, 2018, Oracle, MariaDB Corporation Ab and others.
Usage: ./mysql [OPTIONS] [database]
Default options are read from the following files in the given order:
/etc/my.cnf /etc/mysql/my.cnf ~/.my.cnf
The following groups are read: mysql client client-server client-mariadb
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