[2022] DICE CM confirms that all Battle Pass cosmetics will never available again at a later date on the store or any other place, if you missed season 1 and 2 you lost them forever. Only the specialist, weapons and vehicles can be unlocked at a later seasons in form of an assignments or quests.

To provide further clarification on this, I was speaking to things as it stands at this moment in time. There may be a day in the future when previous Seasonal cosmetic content is made available through other routes.

However, at this moment in time, speaking to Seasons 1 or 2, the cosmetic rewards that were offered are currently unobtainable if you had not managed to unlock them during that Season.

And as a reminder; all gameplay-affecting items such as Weaponry, Vehicles, and Specialists will always be earnable for free within each Season and if you missed out on them during that specific Season - they will become obtainable through missions at a later time.