If they're saying we'll be an interstellar spacefaring civilization in much less than 300 years, they really buried their lead :)
If you think we can't reach Kardashev scale I in 300 years you are really pessimistic!
We have, right now, the technology to go visit other stars. It would take a sizable amount of the world's GDP but it is possible. I certainly hope that in 300 years we will have explored other systems!
Mass of a hydrogen atom: 1.67 x 10^-27 kg
So there are 1.2 x 10^57 atoms in the sun. And we need the sun.
The mismatch is caused by someone extrapolating an exponential trend in one area well into the future, ignoring physical reality. Anyone with a good grasp of high-school physics should have noticed this before the slides were released.