Monostable stable state
No, C1 does NOT charge "instantly" when the output of the first gate goes high (BTW, where are your reference designators for the gates?). Because it is discharged, both ends of C1 go high when the gate goes high, which drives the input of the second gate high and its output low. Since this output is fed back to the first gate, this insures that the output of the first gate remains high.

However, because there is now a voltage across R1, a current begins to flow through it and C1 does start to charge up with a time constant of 1 &micro;F &times; 100 &Omega; = 100 &micro;s. As the voltage across C1 increases, the voltage across R1 and at the input of the second gate decreases. Eventually, it decreases enough that the output of the second gate goes high again, which allows the output of the first gate to go low if the other input is also low at that time.