From a conceptual perspective, very low quiescent current (aka idle/standby current) when unactivated is entirely achievable. What your design will need to do is assess how much each component will draw at idle, and if it's too high, then you may need to have gates which turn off those high-draw components when idling.
From a cursory Google Search, the DFPlayer Mini datasheet shows a standby power of 20 mA, which far too high. A forum post shows that if the sleep mode is enabled using the serial interface, current drops to 0.4 uA. This is much better.
For the 555 itself, you mention an astable oscillating configuration, although I'm wondering what your intention for the 555 is. Ostensibly, the DFPlayer either needs a brief pulse to start playing (roughly "edge triggered") or needs to be kept active for as long as the music should be playing (roughly "level triggered"). In either case, a 555 in a one-shot configuration would make sense, since an astable oscillator would imply the music would restart on its own every so often.
If you're insisting on the 555, then you may not be able to access the sleep mode in the DFPlayer Mini. So your option might be to gate the DFPlayer so that it only gets Vcc power when the 555 supplies it, probably using a MOSFET. Alternatively, using a cheap microcontroller would let you control the DFPlayer Mini via serial. Your microcontroller could then also receive the signal from the vibration switch and come out of deep sleep to issue commands to the DDPlayer.
The ATTiny uC and MSP430 uC families can draw as low as microamps or even nanoamps in some low-power modes. So that neatly addresses the standby current.
What you'll also have to assess is the active current, or how much the music player draws when it runs for however long. This should give you an idea of the total lifetime for your application on a single battery charge.