555 timer capacitor charging order
When the cap is discharged, you are in a situation similar to this:



simulate this circuit &ndash; Schematic created using CircuitLab
Since the cap is discharged, it is initially at zero volts.  So what is the voltage at pins 6 and 2?  Zero.
Of course, this starts changing as soon as current starts flowing into the cap.  At first, all the voltage is dropped over the resistors, but as the cap starts to fill up, its terminal voltage starts to rise from zero.  Now less and less current is flowing over the resistors, therefore less and less voltage is being dropped by them.  Eventually the voltage across the cap (and therefore on pins 2 and 6) is high enough to trigger the comparators.
Think of it this way:  The voltage can't get from the power rail to pin 2 or 6 without passing current through the resistors.  Ohm's law tells us that current through a resistance drops voltage.
Let's look at the case when the capacitor has just finished discharging:

Image Source
Let us agree that when the capacitor is discharged, there is the same voltage on both its terminals.  Let us also agree that the voltage seen at pins 2 and 6 is the same as the 'top' of the capacitor.
Now the capacitor starts charging as current flows from the 5 V source, through the resistors, and into the capacitor.  Since this current is limited by the resistors, the rate at which the capacitor fills is called its RC time constant.  i.e. This voltage rise is defined by the size of the resistors and the capacitance.
As the capacitor fills up, the voltage on the upper terminal starts to rise from ground.  Remember, whatever voltage this terminal is at is the voltage that pins 2 and 6 are seeing.
Eventually this voltage is high enough to trigger the comparators, and the discharge pin gets grounded and discharges the capacitor, and now the whole thing starts over.