Code First or DB First and what design pattern to connect to multiple database instances with exactly same schema

I am designing code for a new project. There would be many client specific databases(to store employee of the client org) with EXACTLY same schema.And there would be a master database which will store db connection string against client_id. Depending on employee from which client is requesting, connection string will be fetched from master db(for master db the conn string will be in web config) and then client specific db will be connected to validate client's employee id/password

Can someone suggest if I should use code first or db first and what design pattern I should use here?