Are you able to start building your recruitment list as soon as the new season starts?

You can begin building a list of next season’s recruits during the season.

You can start building the recruiting list as soon as the season starts, however, your vision may change at the end of the season and before the recruiting period starts.
This could cause some of the recruits you previously saved to no longer be in your vision or for higher rated recruits to now be within your vision.
It is generally best to build your recruiting list just before the recruiting period starts.

I start building my list when the win-loss records on the office home screen flip to 0-0. Your list will be accurate at that point because it will have been compiled with your updated "vision."