fm transmitter booster - can it even work?
This circuit is a classC amplifier, reactive load line, with PI filter "CLC" matching the transistor collector to the load.

ClassC is biased OFF, unless you provide large enough input drive voltage; you need +- 1 volt (probably) to get lots of power output; +-1v is about +6dBm across 50_ohms load. Here your load is: 300 ohms || very nonlinear Cmiller. You may benefit from a PI stepup network; as example, your output PI is stepdown, so use that in reverse at your base.

The classC is viewed as high efficiency, conducting for &lt; 180 degrees, causing lots of distortion. 

The output PI filter has purpose of

(1) removing some of that distortion

(2) converting the available carrier energy from the high collector impedance to a much lower load/antenna impedance.

You can work with 33pF Cin. As you use a PCB to implement this circuit, the inductances will change with various layouts, and the value of 33PF may change.

Why does the transistor not blow up? The RFC from +12 to collector is nominally infinite impedance at the input drive/switching rate. Impedance of 1uH at 100MHz is j628 ohms, thus maximum current is 12v/628 or ~~ 20mA.

In USA, the FCC has various regulations about using circuits like this.