You will have to use the continue timeline option on your first playthrough to start the game for a second time. There is nothing you can do to end the time loop on the first try and the game ends when you reach the end and communicate to yourself about the time loop.
Is there an ending to Oxenfree?
Oxenfree features a number of interchangeable ending scenarios. Decisions made in an individual playthrough effect the final outcome for the game. Please note that there are spoilers aplenty ahead! You've been warned!
How many endings does Oxenfree?
With 10 possible endings, Oxenfree is extremely replayable, as you can return to see how the smallest decisions (to help one person over another, for example) impact the timeline.