How does one derive the Schwarzschild Metric as a solution of squashing matter together? So we have $2$ statements of a blackhole. 


*

*If we postulate a spherically symmetric Lorentzian metric then the solution is the Schwarzschild Metric. (Birkhoff's theorem)

*If I squash enough matter together a blackhole is formed.


How can I show statement $1$ is a solution of statement $2$? Or what initial conditions give rise to singularity of the type seen in the Schwarzschild metric (without starting with one)?
 A: In the question a couple of misconceptions are mentioned. 
First of all, Birkhoff's theorem says the following: 
"The external gravitational field of a spherical-symmetric mass distribution is equivalent to a field of a pointlike assembly of the total mass in the center."
The Schwarzschild metric can be applied to the outer empty space around all types of non-rotating spherical mass distributions. So it applies not only to a non-rotating black hole, but also to the metric around the sun for example. 
From this it is clear that from  point 2) is not a prerequisite of point 1) respectively 1) can be concluded from 2). 
A black hole is not necessary for the establishment of a metric which equals the Schwarzschild metric. 
Actually the primary "singularity" of the Schwarzschild metric is at $r=\frac{2GM}{c^2}\equiv r_{schwarzschild}$. In order to see it clearly, the metric is given here:
$$ds^2 = (1-\frac{2GM}{c^2 r})dt^2 - \frac{1}{1-\frac{2GM}{c^2 r}}dr^2 -r^2 d\theta^2 -r^2 sin^2(\theta) d\phi^2$$
At $r=\frac{2GM}{c^2}$ the metric component $g_{11}$ behaves $g_{11}\rightarrow \infty$.
So actually the Schwarzschild metric in its original form is only valid for $r>r_{schwarzschild}$. So a priori the Schwarzschild metric does tell us nothing what happens inside a black hole, respectively its singularity at $r=0$ (but it tells us the metric outside of a non-rotating black hole without charge).
However, the "singularity" at $r=\frac{2GM}{c^2}$ is only a problem due to (unfortunate) choice of coordinates. By a change of coordinates it can be extended to another metric called Kruskal-metric which also extends up to $r=0$. 
By the the way I would consider a (in cartesian, polar or spherical coordinates written) Lorentzian metric as flat (here in spherical coordinates) :
$$ds^2_{Lorentzian} = dt^2 -dr^2 -r^2(d\theta^2 + \sin^2(\theta)d\phi^2)$$
