Did Juno start off its course on the ecliptic plane from the earth orbit and then left it at insertion to Jupiter's orbit over its north pole or it was always in that plane?
The plane of the orbit around the Sun is not directly related to the planet-relative plane of the hyperbola on approach to Jupiter, or correspondingly the orbit around Jupiter after orbit insertion. The plane and shape of the orbit around the Sun relative to Jupiter's equatorial plane determines its approach declination to Jupiter. That is essentially the negative of the latitude on Jupiter of your atmospheric entry point if you tried to target your spacecraft to hit the center of Jupiter. The magnitude of the approach declination limits how equatorial the orbit can be, but not how polar it can be.
On approach to a body, your target can be anywhere in a plane perpendicular to your approach trajectory, at essentially zero cost. That plane is called the B-plane:
For convenience, you target a point on the B-plane that you would intersect if the planet were not there, or if it had no gravity. You actually cross the B-plane inside of that point due to the planet's gravity. You get to pick how far from the center of the planet your target point is, and the angle of that point anywhere around the planet. The distance from the center determines your closest approach distance, or your atmospheric entry flight path angle. The angle determines the plane of your planet-relative approach trajectory, which will be the plane of your orbit.
Your approach declination defines a line through the center of the planet entering at a latitude equal to the negative approach declination on one side and exiting at a latitude equal to the positive approach declination on the other side. That line is labeled "S" in the diagram. Imagine a plane that contains that line, and you are allowed to rotate that plane around that line. Those are your allowed orbit planes. One such plane is the "Trajectory Plane" in the diagram. Since your plane must go over the latitude of the magnitude of the approach declination, your orbit plane inclination to the planet equator cannot be less than that. If it were less than that, then your orbit could not go over that latitude.
Juno's approach declination was about 8°. Then by choosing how you target the Jupiter closest approach, which can be anywhere in a circle around Jupiter, you can pick any final orbit inclination from 8° (prograde) to 90° (polar) to 172° (retrograde).
After orbit insertion, you can do maneuvers or swingbys of satellites to change the orbit plane, e.g. if you wanted to be more equatorial than the approach geometry permitted. Cassini is the champion of this, having dramatically changed its orbit plane many times over the course of its mission at Saturn, using Titan gravity assists.
As noted in comments, by selecting the launch time and initial trajectory, any relative inclination between Jupiter and the spacecraft could be achieved.
That said, while plane changes measured in degrees are indeed expensive, for an orbit that goes out to 5 AU, one degree of relative inclination corresponds to a deflection of something like 12 million km.
If, after Earth flyby, mission control had realized that Juno was on a direct collision course with Jupiter, they could have done a 1-meter-per-second correction "northward"; Juno would then pass over Jupiter's North Pole at a distance of about 60,000km. In the solar frame of reference it's still a low inclination orbit; in Jupiter's reference it's polar.
Basically, Juno came in towards Jupiter from slightly below it. This allowed it to slow down into an orbit which takes it around the poles of the planet. Over the course of its journey to Jupiter, it was at a very slight angle, relative to the plane of Jupiter's orbit. This angle was determined by the flight engineers at its launch, and refined by two deep space maneuvers and an Earth gravitational assist flyby. This slight angle was enough to put the craft below Jupiter, because its journey was very long. More information about Juno's trajectory can be found in Spaceflight101's article, which includes a Juno trajectory animation.
I estimate the launch time and coordinates must have been optimally designed so that the gravity assist would already position Juno in an inclined plane much more than what was needed ultimately but adjusted over the long trajectory by the pull of Jupiter into correct entry point.
NASA would have two tools to angle the shot: earth's orbit and its axial rotation.
I'd assume they designed the trajectory purposely not in the plane of solar system at all but in an inclined plane winding up and down the apogee of its orbit as needed riding the great roller coaster. Hats off to Isaac Newton.
quote from Wikipedia page on Ulysses probe
to change the orbital inclination of a spacecraft a large change in heliocentric velocity is needed. However the necessary amount of velocity change to achieve a high inclination orbit of about 80° far exceeded the capabilities of any launch vehicle.
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