Train travel and visa

We are one American and one Norwegian landing in Beijing and taking the train to Vietnam and coming back in for a flight out of Beijing the same way 15 days later. The train takes 2 days. Is there a scenario you can propose where we won't need to purchase two entry permits as onward travel is our ultimate goal?

For instance, if I fly out of Beijing to Vietnam instead within 24 hours and fly back in to leave out of Beijing, can I be exempt?

Any advice appreciated!