This is how close the Moon was to the Earth about four billion years ago. Today’s view of the Moon today is to the left for comparison.
The Moon affects the Earth with tides, in the water and in the crust. This gravitational energy slows the Earth’s rotation. Being 81 times more massive, the Earth slowed the Moon’ s rotation to once every 27.8 days, called tidal lock. This lost energy had to go somewhere, so, being less massive, the Moon’s distance from the Earth had to take up the slack; energy is conserved. A higher orbit takes more energy, so the Moon moves away about one inch/2 cm with every 27.8 day orbit.
This has been measured very precisely. There is a laser reflector on the Moon set there by the Apollo astronauts used to measure this.