How do we get the UFO to spawn so we can go to the moon?

There is many steps, you need to drive the UFO. If the UFO came to pick you up earlier, it was a player playing as the UFO.

Look around the map, you need to find 2 things ; a secret code and a secret garage. 

Hint as to where the secret garage is ; it's close to where the aliens hang out.

You don't need to pilot the UFO yourself, I've seen plenty of players park the UFO near the spawn to let others hop on, then taxi them up to the moon.

Edit: In fact if they let you hop on the UFO, you can use chat to ask them to take you to the moon. There's a chat phrase that's "Please take me to _____" or close to it