If you haven't got the name, forget it.
I would, about 24/48hrs after. Email is a pretty sh1t way of building a rapport - phone works much better. They may have never heard of you, but they will presumably have received your email - and if they decline your pitch, you get to ask them what kind of other stuff they may be looking for.
How you pitch is also fairly critical. These people are not going to want to read huge email propositions, so make your email header pertinent and make the pitch short but relevant. If the ed wants a further synopsis, they can ask for it in response.
I work in an entirely different industry but part of what I do involves getting people to take me seriously with a view to them at least recommending me for something. I never email unless I really have no choice. I always call first, then email, confirming all the details we talked about on the phone. Cold calling is a tough experience but it can work.
Take loads of drugs and write while out of your mind. It worked for Hunter.
I love writing but no longer make a living out of it... in fact, I enjoy writing more now it's not my job.