Simply; The sound gets clear. It at first sounds smeared.
Technically; Several things happen. The major thing is; during the break in period, the dielectric material (the insulating material) interacts negatively with the signal flow. The dielectric absorbs and releases energy as opposed to passing it through the capacitor. Uncooperatively, this is occurring at chaotic intervals.
This sporadic interaction is changing signal flow through the capacitor. However, the dielectric material changes over time as voltage is applied to the capacitor. The voltage creates heat, and a polarized skin forms on the surface of the dielectric (called skinning).
The dielectric then has a path through which to absorb and release energy, and does so at the correct times due to the formed path. (Like a path through a forest that is traveled over and over). Also over time, as voltage is applied to the conductors (the foil) the metal tempers, creating patterns as well (electricity will take the path of lowest resistance).
There are other reasons like skin effect (With an alternating current, there is a delay in the magnetic field’s response to the change in current and the ‘old’ magnetic field tends to push the current towards the outside of the conductor. As the frequency increases, so does the effect until at very high frequencies the entire current flows in a very narrow skin on the conductor–hence the name).
One other consideration is self inductance (The property of self inductance is a particular form of electromagnetic induction. Self inductance is defined as the induction of a voltage in a current-carrying material when the current in the wire itself is changing). Although this is a non-inductively wound capacitor; meaning, careful attention is made to not produce inductance with the design, there is an inductance due to the alternating voltage.
Every electrical component has a break in period. Some are more noticeable then others. Signal carrying components are the most obvious. It will take approximately 100 hours of operation for the capacitor to function to full performance.