Yep, youth team appears when you have Youth Center(YC) level 3 and at least 10 players at u21 age.
But after getting this it's not good to rush with next YC levels, concentrate then on Training Center and Stadium. Before YC level 10 your players probably will not reach to first team, so it's better to buy some cheaper u21 players with talent between 4 and 5, who can progress and maybe reach to first team or be sold at higher price later. Lower YC products will be bought by bots or bank. Currently you have 7 u21 players and 2 who will be removed after some days, you'll get 2 bonus players when YC3 is ready and then have to wait another.
U21 league is only for giving training experience to young players, results mean absolutely nothing and non-competitive, no awards even if you win all u21 league matches, just some missions completed. For competition is u21 cup.