If an observer's distance from a light source exceeds the distance required for light to travel to the observer, and we have the advanced technology required to see something that far away, and also know the exact location in space to look (although data transfer speeds are bottle-necked by light-speed, but let's imagine that bottle-neck doesn't exist...), could we theoretically see the start of that light source
Assume that the sun exploded right now. We would see the effect of it after 8 minute later, since that is the time it takes for the light travel between the sun and the earth.
This is true for any event. Even when you look at the mirror you are seeing the past. We always see the past. How past, well it depends on the distance between the source and the event (At this point things can be affected due to expansion of the universe, which is an important factor in large distances)
You would also need to know the location of the Universe's first light source
There is no such location in the universe. In other words, there's no direction which you can point at and say "that's where the universe started". Think about the surface of a ball. You are a 2D creature living on the surface. There's no physical center for this surface. The center lies inside the ball which a 2D creature can never point/reach.
but if we did, could we theoretically go one step further and go outside the radius of first light emitted from the Universe's center and watch the birth of the Universe?
We cannot because of there's no such place. There's no center for the universe.
And btw CMB is not the "first light". There was always light (photons). In the early universe, these photons were coupled to the baryonic matter. Which implies that the photons were always interacting with the particles. When they decoupled from the matter, these photons became free and that is the CMBR. It's just an event that occurred in the early universe. If we had some sort of a superpower to detect very low energy neutrinos (about $1.9K$) we would see the Cosmic Neutrino Background which occurred around $1s$ after the big bang. Meanwhile, the photon decoupling (Event that created CMBR) occurred around $300,000$ years later.
Theoretically, you can go outside of our observable universe. But thats a completely different story from what you are describing.