Hey, The only way to purchase Season of the Hunt now is by puchasing/upgrading to the Beyond Light Deluxe Edition.
Pretty much can't be done on a free to play account. Must have paid DLC. If you follow these steps, you should get the Hawkmoon 2.0. https://www.eurogamer.net/articles/destiny-2-hawkmoon-feather-locations-as-the-crow-flies-7004#section-1 The mission is S tier solo. Good Luck!