Hi. I'm currently running two 5e games for 1st levels.
They are both at a point where a new character could join them.
The first is the Secrets of Phandelver from the boxed set.
link to another game
The second is the Road to Shamballah. The characters are a accompanying a group of monks seeking the legendary Shamballah. They left the monastery two days ago and have arrived in a town.
link to another game