I would like to understand how (if possible) the measles virus could start to infect a population that was theoretically isolated from any other population group. Put another way, can the measles virus develop within a person without external influence/inputs?
The question could be rephrased
Can a measle virus be created anew and not via reproduction from another virus?
The answer to which is "no".
The falsified idea that new life forms can jump pop up out of nowhere is called spontaneous generation. Spontaneous generation do not occur.
Note however that sometimes it may look like as if a new epidemic came from nowhere. The reasons is due to natural reservoir.
A natural reservoir or nidus (the latter from the Latin word for "nest") is the long-term host of a pathogen of an infectious disease.
An asymptotic carrier can be used as a natural reservoir
An asymptomatic carrier (healthy carrier or just carrier) is a person or other organism that has contracted an infectious disease, but who displays no symptoms.
These reservoirs can keep the viruses (or other pathogens) alive in while from the outside it looks like the disease has been eradicated. At some point the virus can spread again making it feel like it came out of nowhere.
[..] my confusion is on how a population gets the first instance
There is no clear first instance. Modern day measle viruses evolved from an ancestor that was not the modern day measles. Just like there was no sudden first human (or any other species). There were just ancestors that evolved to become what we now call modern day humans.
You might want to have a look at an intro course to evolutionary biology such as understanding evolution by UC Berkeley for example.