The trick is that stars are created when gravity acts on clouds of gas and compacts them. In the early stages of its life a star spews out vast amounts of water at very high pressure.
Water under very high pressure (50,000 atmospheres or higher) takes the molecular form of a double-helix ~ in very long chains.
A new born star undoubtedly spews out all sorts of other chemicals in long or short chains at the same time. The chemicals of life are all water soluable. Add 2 and 2 together and there you have it. Not being an xenobiologist I can't take you any further into the details.
Which is to say that we may well live in a universe where a fundamental fact of existence is that new stars spew the seeds of life into their own near environment. Sometimes life prospers. Sometimes life doesn't prosper. It may well not need to be shipped in from some other solar system ~
“Genesis posits that it all began with a big bang.”
Really? Chapter and verse, please.