To sustain oscillations, the LC loop (or string) must do these things in a cycle:
* Alternate between delivering a little (or no) bias current to the transistor, then a lot of bias
* Receive just enough jolt from somewhere, to gain back whatever energy it lost
Considerations to help achieve the above:
* The control network needs a certain degree of isolation from the supply rails
* A large capacitor needs more current than a small capacitor, to create the same voltage swing.
* A small coil needs more current than a large coil, to create the same emf and the same flux intensity.
* The transistor usually needs a certain amount of bias current in order to get the action started. The bias level needs to be adjustable, hence a potentiometer is handy for this purpose.
-------------------------
Your layout has some resemblance to a Clapp oscillator. It is distinguished by having a coil and cap in series. Operational circuits have a few more components added.
You may be able to get your setup to work, if you can fulfil all the conditions. Don't be surprised if it requires some reconfiguring. See if you can jolt it into operation somehow. There may be a few oscillations afterward, even if they decay quickly.
I recognize you are using Falstad's simulator. It is easy to use. I like it and I use it as an alternate to my own homebrew animated simulator.
I have a video of Clapp oscillators in animated simulation on Youtube:
https://youtu.be/wKnarrvynIw