I see the father coming into NY in 1904 and says he is going to Antonio.
Now, it's interesting.... it may be that Antonio went back to Italy. There is an Antonio Albanese on the manifest of the SS Republic sailing from Naples in 1906 in April to NYC. He is on line 8 and stamped page 11. He is 26 years old. He was born in Molise. He is going to his brother Paolo Albanese in what looks like Palisade Park, NY (which is in NJ!). Column 15 of the manifest which asks whether ever before in the US and if so when and where indicates he was in the US from 1903 to 1905 at Palisade Park. Now, the line with this name is **crossed out** meaning he booked passage but never sailed.
Added note: There are other entry points into the US besides Ellis Island. I see an Antonio Albanese age 25 arriving through Canada in June 1905. Ancestry has the border crossing information with 2 separate documents. He had been in the US previously..... looks like same time period.
and... there seems to be lots of Antonio Albanese on Ancestry's immigration records for the time period you targetted.