Is the moon the closest object in space to earth true?

Except for meteors, The Moon is, generally, the closest natural object in space to the Earth.

Usually. On rare occasions, small asteroids zip by the Earth somewhat closer to Earth than the Moon is - and occasionally, a LOT closer. There was an asteroid in late 2009 that passed by the Earth at a distance of less than 100,000 miles. In 2029 and again in 2037, the asteroid Apophis will pass by the Earth at a distance of under 20,000 miles.

If we include meteoroids, then no. Every day, the Earth is struck by tens of thousands of asteroids, and there are probably hundreds of thousands more that missed by some fairly small distance.