1) The capacitor charges slowly,
2) until the left-hand node is at a high enough volt level to turn on the NPN transistor.
3) When the NPN turns on, it pulls the PNP bias low, turning it on.
4) The PNP conducts a burst of current, which goes through the speaker.
5) The capacitor receives a current burst, charging it in the other direction.
6) The process repeats.
To grasp the operation of an oscillator, it is especially helpful to watch it in animation. To see current flowing in the wires. Not to mention scope traces on several components.
This is a screenshot of the schematic as I laid it out in Falstad's interactive animated simulator.
To see what I see, and see it running on your computer...
Click the link below. It will open the website falstad.com/circuit, and load my schematic above.
https://tinyurl.com/m8756cs
Notice the colors which indicate volt amplitude and polarity.
The left-hand node goes as low as -1.8 V for a time (even though the supply V is positive).