As a kid, having been given a 100,000 Hertz crystal of size 1" by 1" by 2" from some WW2 military radio, I tried repeatedly to get that beast to oscillate, listening at the 5MHz WWV channel for some interference or beat note that would indicate successful oscillation.
I never could get oscillation.
The challenge with a crystal is the interface with outside circuitry.
One standard method is using PI_filtering mindset, where two external capacitors provide a closed_loop path for circulating currents.
Each end of the crystal is shunted to Ground; the size of the capacitors is proportional to the internal electrode_to_electrode capacitance; with thick quartz needed to resonate at 100,000 Hz, the spacing is high and the electrode_to_electrode capacitance is low, so you need only a few picoFarads lumped C at each end of the crystal.
As a kid, having had vector algebra and complex number math in school, I could have written the small_signal model of various ARRL (HAM) oscillators, and perhaps extracted the conditions for successful oscillation. Maybe.
But my brain was not ready for small_signal modeling.
The 2_external_cap PI_filter interface to the quartz crystal has the useful behavior of INVERTING the voltage. This allows very simple one_transistor amplifiers, of common_emitter or common_source (of common_cathode) configuration, to be used.
As a kid, I did not have that understanding. Thus my 100,000 Hz circuits never oscillated.
===========================================
How to start the oscillation? how does one make a bell ring, or a crystal goblet ring? you lightly and briefly tap it.
And in electronics, there is random electron noise, as the electrons very quickly jump orbitals inside the atoms. That is the "tap" needed.
Probably bigger taps come from switching regulator spikes. Or just turning on the power. But the random and very-fast electron jumping around is always there.
HINT: a quick tap makes ANY bell or ANY goblet ring. That quick tap has a special name IMPULSE, meaning has some energy and very fast (ideally zero) time duration.
Thus the very_fast impulses make ANY QUARTZ CRYSTAL ring and ring and ring, as the transistor provides the boost in energy inside the quartz.
============================================
Here is link to a previous answer, to explain the PI_filter usefulness. Scroll down, past the simulation, and examine the last two circuits.
How do crystal oscillators start?