If you do not purchase the Battle Pass, you only earn rewards from the Free Pass.
The Free Pass offers a limited number rewards, not as many as with the Battle Pass. But you get them for free.
You can buy the Battle Pass at any time to retroactively unlock all rewards up to the current tier you are on. Though it is more beneficial to buy the Battle Pass as early as possible since you will be progressing faster because of all the extra challenges and experience boosts.
See: Battle Pass FAQ