Corner speed is everything, try to power through the corners this is what give you the speed down the following straight.
A good tip is to put your weight as far fwd as possible when exiting slow bends or starting, this gives the very underpowered karts every possible chance of picking up revs as soon as possible.
You can also use the fact that the kart has rear brakes only as a good way of sliding it in sideways (although not too much) as you can scrub too much speed off.
It is worth noting that as the race goes on the tyres will start to get up to temperature and you should feel the kart getting more grip (yes even on indoor circuits) if you do feel this start to push a little harder.
Try to get as many places as possible at the start, it's never easier than then to overtake.
Lastly relax and enjoy.
best fun you will have with your clothes on