In my world, humanity reaches their new home among the stars by way of a portal that pops into the solar system one day. This portal instantaneously transports those who enter to a place that is located a jaw-dropping 6 gigalightyears (six billion lightyears) from Earth.

But the astronauts traveling there don't know that. Would it even be possible for them to determine how far they had been transported? And in what direction?

I would imagine that they'd look for known galaxies, or perhaps look at the cosmic microwave background for clues. But those things might appear radically different, considering the astronauts have been transported over a billion years into the past (or is it the future? Wormholes confuse me).