They are not the same age. If you had a chance to see the stargazing programme earlier this week, Brian Cox was holding a meteorite which had come from outer space and had been dated at many thousand years older than the Earth.
The universe is currently supposed to be about 13.7 billion years old Flobadob. The Earth is only about 4.6 billion (4,567 million years) from radioactive dating.
The universe supposedly formed from the Big Bang and the solar system and Earth accreted under gravity from a nebula (a gas and dust cloud). That was formed by the explosions of nearby stars that had run their lives and died in supernova explosions.
One would need to be a creationist to consider they might be the same age. Otherwise before a planet can form the universe had to be already there in which to bring the matter together to form the planet.
Following the big bang the Universe consisted of very nearly 75% Hydrogen, 25% Helium and a trace of Lithium. All other elements had to be created in stellar cores and supernovas. It therefore follows that planets could not form until enough material had been synthesised in the stars. Earth appears to have formed at almost the earliest possible time that it could have, which, as noted previously, was some 9.2 billion years after the origin ofthe Universe.