That's not nessisarily true. Single celled organisms have a rather fluid exchange of genetic information even our 'single cells' are really several different organisms. It's possible life evolved many times on earth and current single celled organisms and thus all life has a mismatch of ancestors.
Further, life may regularly evolve even today, but simply get eaten due to the stiff competition.
PS: We know life evolved at least once, but the high end could be multiple times a second on earth.
It's also possible it evolved elsewhere and rode here on a meteor - or was brought here by some other lifeform several orders of magnitude more advanced than us, using earth as their own cosmic terrarium.
It's good practice to assume the simplest possible solution. However, the full range of the full range of what might have happened is ridiculously large.
But all lifeforms we know evolved from one common ancestor, it's one tree of life. As far as we know life evolved here only once.
So we know that once life happens it can become completely ubiquitous, but it doesn't say anything about that crucial first step.