The prince had always longed for a sibling, it was--- hard-- to say the least; growing up with the suitors who only wanted his mother for her body and the throne. All he had growing up were the suitors, who were awful, and his mother, who he loved.
So imagine his excitement when he saw his father for the first time- then even more excitement when Odysseus opened his cloak after killing all the suitors, revealing a little kid. Later than night Odysseus explained to Penelope and Telemachus that he found the child abandoned and decided to take care of them, Penelope had no problem with it at all, more than happy to open her heart to the young one, and Telemachus was THRILLED.
About a month goes by and even though the kid was still very scared of everything around them, Telemachus adored his new sibling.
As per usual it was early in the morning and Telemachus wanted to see his little sibling so he quickly woke up, got some toast and grape juice for the kid, and walked into the little kids room that had already been decorated with things they've shown interest in. "Hey, buddy!" He greeted quietly but with a bright smile.