Based on our current understanding of physics and the limits of the natural world, the answer, sadly, is no. According to Albert Einstein's theory of special relativity, summarized by the famous equation E=mc², the speed of light (c) is something like a cosmic speed limit that cannot be surpassed.

How close to the speed of light can we get?

The most energetic particles ever made on Earth, which are protons at the Large Hadron Collider, can travel incredibly close to the speed of light in a vacuum: 299,792,455 meters-per-second, or 99.999999% the speed of light.

Can we go 1% the speed of light?

It's possible to get something to 1% the speed of light, but it would just take an enormous amount of energy.