I did some research in the Birth registers of Amsterdam.
In the index Births Amsterdam 1823-1832 shows 2 possible Jan's:
Johann Christian Verbeek 3 nov. 1823,
Jan Verbeek, Birth Date 18 Sep 1823
But they can't be the one you're looking for:
the First one had another first name of the father and seems also to stay in NL.
en the second one were no parents mentioned because he was a foundling.
But because it happens that not always the exact birth year is mentioned, I also looked in the Birth Index Amsterdam 1813-1822
and there I find Jan Verbeek born 9-3- 1820 -
and his father is a Jan Verbeek, mother Klaasje de Vries.
His mother died before april 1851, father is then still alive, but he could have died not long afterward but that's still an open question.
His father Jan is a tobacco worker.
Do you have an idea when your John left Netherlands ?
and did he get children, do you recognize somehting from Klaasje in the names of children?
This is the only one I can find nearest to 1823.
I also looked on Verbeck and Verbeeck, but no births on that name.
Verbeek is a very common name , so that makes it not easy, especially also because you don't know the mothers name of course.
Do you have more then one source that says in which year he was born?