Even without magic repulsorlift, the X-wing could make it to orbit the same way real world rockets do: climb up until the atmosphere thins out enough that it no longer slows you down too much, then accelerate sideways until you're basically in orbit.
The X-wing data sheet might show a single "maximum atmospheric speed", but in practice "atmosphere" is relative: not only do different planets have different atmospheric densities, but the atmosphere (of any planet that has one) gets thicker as you go lower and thinner as you go higher. The speed shown in the data sheet might a maximum rated speed for flight in the low atmosphere of a typical earthlike (i.e. human-habitable) planet, but as the X-wing gets higher, basic physics says it can go faster.
Besides, even if you were a really cautious pilot and really didn't want to exceed the manufacturer's rated atmospheric speed limit anywhere inside an atmosphere, you could just climb straight up at that speed1 until you get to a point where you're no longer considered to be "in an atmosphere"2 and then accelerate sideways to orbital speed.3
1 - Which, even without using repulsorlift, the X-wing's ridiculous 3700 G engine acceleration should be able to easily maintain against any planet's gravity.
2 - Of course, this is an arbitrary matter of definition; the air density drops gradually with altitude, but there's no sharp line where it would suddenly reach zero.
3 - Which, with the X-wing's still ridiculous engines, should take seconds at most.
Ps. This is actually an issue that's encountered in real world spaceflight, too. If there was no atmosphere in the way, the most efficient way to launch a rocket to orbit would be to accelerate (nearly) horizontally straight off the launch pad as quickly as possible until you reach orbital velocity (and then perform a small circularization burn at apogee to ensure that your final orbit doesn't intersect the launch pad).
However, if you tried to fly a rocket at anything even close to orbital velocity in the Earth's lower atmosphere, air pressure would flatten the rocket into a pancake and compression heating would then burn it to a crisp.
You could try to solve these problems by building a stronger rocket able to withstand more pressure and adding heat shields to protect it, but that would make the rocket a lot heavier, which is the exact opposite of what you want.4 And it still wouldn't solve the remaining problem, which is that the same air resistance that's trying to crush and burn up your rocket is also slowing it down very quickly, much faster than your engines can accelerate it.
Instead, the way real orbital rocket launches solve this problem is by first accelerating relatively slowly (almost) straight up. (Conveniently, real rockets accelerate slower at first anyway, since they're loaded down with more propellant, with their acceleration increasing as the propellant is burned and ejected and the rocket gets lighter.)
As the rocket gets higher in the atmosphere, the air gets thinner and offers less resistance. The launch trajectory of real world rockets is planned so that, as that happens, the rocket gradually turns more and more horizontal, allowing the engines to start accelerating the rocket horizontally to orbital velocity instead of just pushing it upwards against gravity.
If you watch a video of a rocket launch (which we have plenty of these days), one of the moments likely called out in the video is "max Q", or the point of maximum aerodynamic pressure. Basically that's the point where the rocket is high enough that the atmospheric density starts dropping faster than the rocket's speed increases. It's also the point where the rocket experiences the heaviest loads on its structure, and thus the point where the rocket is most likely to break if you didn't build it strong enough. (That used to be a serious risk with early space launches. Fortunately we've gotten pretty good at rocket engineering, and that almost never happens anymore.)
Some rockets will even temporarily throttle down their engines before max Q to deliberately keep the rocket's speed from getting too fast and the aerodynamic pressure from getting too high. Once the rocket is past max Q and the air is thin enough for the aerodynamic pressure to start dropping, they'll throttle the engines back up again and start building up orbital velocity for real.
4 - Real world rockets don't have anything like the magic engines of Star Wars and struggle to even accelerate their own mass — not to mention any satellite or other useful payload — to orbital speed. In the real world, we still don't even have a practical single stage to orbit rocket, and have only recently figured out how to squeeze enough performance out of lower rocket stages to make it practical to safely land and reuse them instead of just letting them crash into the ocean after doing their job. In practice, what that means is that every gram of mass you can shave off a rocket, especially in the upper stage(s), is precious because it directly translates to more payload mass you can launch.