First line support are there for one reason: They are a shit-filter (by which I mean they filter shit, not that they are shit at being a filter). They will be able to solve 90% of problems by following their script, because 90% of the calls are from people who don't know what they are doing and it is a simple fix. The remaining 10% get escalated to 2nd line to somebody who knows a bit more.
If there was a special number to get through to 2nd line it would immediately get swamped by everyone calling that directly, because everyone knows that 1st line are useless, right? Wrong. They are great at doing what they need to do, with the limits of their knowledge. You have to go through them whether you like it or not. The quickest, painless way to get the help you need is to go through their tests, whether you think they are stupid or not, as quickly as you can, and you will eventually be moved on up the queue.
In your case it sounds like it might have been an area problem anyway, in which case there would be nothing that 1st, 2nd or 3rd line could do about it.