You only get players which are available to sign AFTER your Target Shot has produced players. Additionally, Target Shot does not even start the timer for producing players until it has finished being built. If you upgrade it again the production of players is stopped and will reset and start again only after the upgrade is complete.
You need to check first when the new players will be available, like below:
In my case after the 8 days are finished, I will have 2 additional players appear in my Squad List. They will be unsigned. To do anything with either or both of them I'd need to sign them within 7 days.
EDIT: I've looked and I don't have a pick of unsigned youth players in my squad. They will appear simply as 2 futher players in your Squad list. They will not appear in your Training list - you can't train unsigned players.