Hi,
I think some resistor values are bit off from what I would personally choose, and therefore closed loop gain is not sufficient for oscillations.
I can see, that exactly this circuit drawing you had problems with, including same component values, is circulating around in the web.
Try something like R1=820, R2=R3=100k. That might wake the circuit up. However, the initial amplitude is high, and falls to a small value, when C3 charges up. Therefore C3=1nF gives faster the steady-state oscillations (of low amplitude). But the start-up still behaves the same way, only settling much faster.
Personally I believe this version of Colpitts oscillator is not the best configuration. One on for example page
https://www.electronics-tutorials.ws/oscillator/colpitts.html works well, and I have used that basic topology even in a real product.
-ted
Added note: I tried it with BC337-25 and -40 on ltspice IV, and it did not work too well. Also, with 2N2222 the circuit is too tricky to tweak and likely never would be robust and reliable. Therefore I strongly recommend you to consider the configuration where the tuned circuit is on base "side". (See the link above)