[1] http://www.carbuyer.co.uk/news/150839/new-tesla-model-3-pric...
Doesn't seem like a couple a month right now and at all. Of course it could dwindle fast from here on out, but even if production doubles you'd still be looking at more than just a couple months. And you'd likely see pre-orders go up accordingly as well, I'm sure there's people who haven't pre-ordered because it makes no sense paying $1k to be on a 3 year waiting list, I wouldn't be surprised if waiting lists didn't budge nearly as much as production rates increase. And besides, doubling production isn't exactly trivial despite Tesla's erroneous claims in the past.
A large chunk of the 400k are probably outside of the US, and another chunk are waiting for cheaper configurations.
If you are in the US and order a 'First Production' model (Long Range battery + premium interior) you will definitely not be at the back of a 400k long line.
Going off of this I would assume the parent poster isn't in the USA. In other countries, the Tesla Model 3 isn't expected to start deliveries until 2019.
Sorry, but no. One can be had in just a couple months at this point, and that lead time will dwindle quickly now that they've really ramped production.