We know that Earth came into existence about 4.6 billion years ago, and it is most likely that the other planets formed at about the same time, just after the Sun started shining some 5 billion years ago.
Almost all meteorites date to around this same time, which substantiates this theory of when the planets and solar system began.
Of course, one could say that the solar system began, as did everything else in the Universe, with the big bang, which was a theoretical burst and not really an explosion.
It is now estimated that the Universe was created almost 14 billion years ago.
But the planets, as we see them now, probably came into existence 4.5 to 5 billion years ago.