Any options for leaving the airport?

Hello,
I am an Australian passport holder, my partner has an Italian passport. We have a flight from Beijing to Sydney booked with a 5 hour connection in Changsha.
We are planning to fly into Beijing from Mongolia and were hoping to have some time in Beijing before our flight. I was hoping the 144hr visa free transit would be an option, but now I am reading that we must have a direct flight out of China.
Are there any options for us to be able to leave the airport in Beijing? I don't have enough time to apply for a tourist visa.
Thanks