Starting Oscillation in Sine Oscillator
When the power is turned on, the voltage rises from 0V to 1V, however an inductor doesn't allow a current to change instantaneously.
It isn't a short but an open circuit at first, the current through L1 can only rise slowly.

A picture is worth a thousand words:



C4 is charged up
L1 starts to conduct
L1 is pulling current out of C4
C3 is fully charged, the current in L1 reverses
C3 gets discharged and C4 charges again


This is a view of the time domain, which is easy to understand. However frequency domains and state space can be better suited to do mathematical analysis, look at other answers for that.