I think there is! You need to continue your way through the code first.
To do this, Suppose that you have the following DbContext that EF Db first created for you:
public class MyDbContext : DbContext
{
public MyDbContext()
: base("Name=DefaultConnection")
{
}
// DbSets ...
}
change that to the following to start using code first and all magic tools of it (migration, etc.):
public class MyDbContext : DbContext
{
public MyDbContext()
: base("YourDbFileName")
{
}
// DbSets ...
}
It causes that EF creates a new connection string using SQL Express on your local machine in your web.config file with the name YourDbFileName, something just like the early DefaultConnection Db first created.
All you may need to continue your way, is that edit the YourDbFileName ConStr according to your server and other options.
More info here and here.