All 32 NFL teams are preparing for the 2023 regular season, and nothing happens, not even preseason, before training camp begins. For the vast majority of teams, their training camp dates can vary.
For teams who play early, as in the annual Hall of Fame preseason game, you will report to camp earlier than those who have a standard 3-game preseason. Otherwise, teams have the flexibility to have their camp dates be whenever they see fit.
Who is reporting to camp the earliest? Try the two teams who are playing in the aforementioned Hall of Fame game, the Jets and Browns.