As already mentioned, a fighter-sized SSTO seems impossible given current or near-future technology. The X-15 was that size and it could not remotely achieve orbit, even given an aerial launch and if using external drop tanks: http://www.astronautix.com/graphics/x/x15a2.jpg
The X-33 was a planned 1/3-scale prototype of the VentureStar SSTO. At 285,000 lb gross weight it was not fighter size but at least it was smaller than a bomber. It was not manned, and despite this would only have achieved suborbital velocity: Lockheed Martin X-33 - Wikipedia
Using air-breathing scramjet propulsion is the only conceivable way current or near-future technology could achieve orbit using anything remotely like a large fighter or small bomber-size aircraft. However the research to date shows this is much harder than was first envisioned, and may never be achieved. This is clear from this free online NASA book, Facing the Heat Barrier: A History of Hypersonics (PDF, part 1): history.nasa.gov/sp4232-part1.pdf
That said, some using the Kerbal simulator claim they have built a small SSTO spaceplane. But I tend to doubt the simulation is very rigorous or representative of available materials, propulsion and thermal protection technology. Otherwise there wouldn’t be such a vast difference between that vs all real-world efforts to date.
But your main question involves time-to-orbit and g force. Given a futuristic propulsion system able of achieving orbit in a fighter-size vehicle, there might be no (or few) limits on fuel or specific impulse or thermal protection. IOW to achieve your premise requires such advanced technology it would be essentially like Star Trek.
If you have no real limits on materials, propulsion or thermal protection, the question is really one of human physiology and g tolerance. A key issue is whether human consciousness is required or simply survivability without permanent damage.
You could just boost constantly at 4 g or so and you’d be at orbital velocity and altitude within about 200 seconds: Uniformly Accelerated Motion Calculator
If boosting at 20 g, you could be in orbit in 41 seconds. If in a supine position, this NASA graph indicates roughly 20 g might be survivable for 60 seconds. The person would probably not be conscious after that but he would not be damaged : https://history.nasa.gov/conghand/fig15d5.gif
For a direction injection orbital insertion, no circularization burn (or impulse) is needed, so the above time periods are time to stable orbit.