Ideally you need to feed the tank circuit from a current source and not a voltage source. The output from your 555 is a voltage source so try feeding the tank through a 1 kohm resistor (kind of simulatesa compromise between a voltage and current source). You could even feed the tank via a small capacitor (such as 10 nF) to get voltage amplification but the Q of this circuit may be too high for what you want.
The inverter on the left can be your 555 output.
You could also use a transistor to connect the tank to a (the) DC supply then quickly disconnect it using the transistor. The time period that the transistor is on should be equivalent to half the time period of the resonant frequency ideally.