how large should the output pad driver be to achieve a speed of 500MHz

[seahs]

what are the typical capacitance for output pad, off chip connection wire and input of the oscilloscope?

I am quite new to IC fabrication and unsure about how many times larger I should size the output buffer, compared to the minimum sized transistor.
BTW, I am using STM65nm

 

[mikersia]

You can get 5...50pF range easily, depending on environment,- PCB implementation, length of wiring, oscilloscope type,...

advice 1: forget about 500MHz for simple CMOS driver,- you will see anything but not a clean signal due to inductive noise (~LxdI/dt); see in direction of CML, LVDS, ... differential driver type with line termination;
advice 2: size of driver transistors is defined often not only by electrical parameters, but ESD protection requirements also,- it should be defined in DR document. So clarify importance of ESD requirements primarily and follow or forget it.
advice 3: if IC isn't commercial and you can ignore ESD requirements, size of driver transistors will give simulation/optimization process. In opposite case an increasing skill in IO design with reading/education of a lot papers will be obligatory to avoid disaster.