About the only way you might is if you find a save game file that someone else has posted online. But why not go through the missions? They're pretty fun if you want to take a break away from simply racing around.
You'll need to play a character that can fly. Then, while racing, look for the orange signs that say "fly". You'll see rings floating in the air. Get your character into the ring, sometimes it's as simple as just riding off a ramp, other times, you may have to jump. Once you pass through the ring, your character will fly guide your character through to the next ring and so on. When flying, avoid steering your character up too much - the character will stall (like an airplane) and fall to the ground, costing some speed.
Yes, it is hard, but possible, and it takes practice. You will need to master the technique for making sharp turn. Let's say you need to make a sharp left. Hold the joystick left. Immediately after, apply the left brake. If you apply brake before you start your turn, you will quickly grind to a stop if you apply the brake after you start the turn, you won't slow down nearly as much. Now, wait a few seconds, then release your left break. If timed right, you'll hear a blast of air, go straight in the direction you're character is facing and accelerate.
If I'm making a left turn, I'll start pretty close to the left side. Immediately before I enter the turn, I steer left, apply left brake. Just as I'm near the track's edge, I'll release the brake, but keep steering with the joystick.
As I've said, it takes practice, especially on this track.
In Sonic Riders, Sonic and his friends are on a mission to foil the evil Dr. Eggman and his new henchmen, the Babylon Rogues. Dr.Eggman has created the Ex World Grand Prix; a no-holds barred racing series where the fastest "riders" in the world participate in this tournament. Never one to turn down a challenge to prove his speed, Sonic and his friends join the tournament and uncover Dr. Eggman's true intentions. In Sonic Riders, players race on air boards through 13 amazingly detailed and challenging courses in either single player or 2 player multi-player mode. The innovatively designed tracks are filled with collectables, jump ramps for high flying acrobatic tricks, and long rails for grinding action. Riders will also ride "Turbulence" – waves generated from other riders – to boost their own speed. "Turbulence" can also be used as a moving half-pipe so riders can perform aerial tricks while racing past fellow competitors.