Is there a way to replicate master/slave without disturbing master for dump like mysqldump or cold copy of data files? I'm ok to bring down the instance only once for master to enable log-bin. But there is no feasibility for dump or even cold copy. As I have 400G of data and 1min down time only.
I would recommend Percona's Xtrabackup for this, especially since you mentioned all of your tables are InnoDB. From the page:
The tool will allow you to take a backup without locking innodb tables. It will do a lock to copy any MyISAM tables (such as the tables
I cannot tell you how long it will take on 400GB database, but it should do it without downtime.