Alternate design for an astable 555 circuit
The "closest" sinewave-like signal you can get from the output of a 555 is when the Duty Cycle is 50 %. As much high as it is low. Then when you filter that (for example with an LC circuit) you get something close to a sine-wave.

The 555 in its basic circuit will always give a duty cycle of more than 50% as the discharge time is shorter than the charge time and the output is high during the charge time.

There are several modifications one can make to the basic 555 circuit to fix this. One solution is to use the 555 as a window comparator which is what is done here.

How you get to the 50% Duty Cycle is largely irrelevant. More relevant is to match the signal frequency to the resonance frequency of the LC circuit and to use a buffer as not to load the LC circuit as then Q will decrease and filtering will be worse resulting in a worse quality sinewave.