While setting up a new sequence, you need to add people to the sequence either by clicking the Add People button or via the red "+" button if there is at least 1 contact in the sequence already:
Once you click Add People, you see a pop-up with 3 options:
Select one of these and add people to your sequence.
When you add people from existing, the prospects listed are all available to be added to the sequence, which means that any contacts associated with a different sequence will not appear. Select the desired people and add them to the sequence.
If you need to add new contacts to an existing sequence, simply go to your Sequence - People tab and use the red button to add more people: