The best site for Dutch records is:
https://www.wiewaswie.nl/en/home/That will take you to the English language pages.
I did a quick search for any Hammer, 1860-1870, in the province of Zuid-Holland (South Holland), which includes Rotterdam.
4th September 1866 birth for Jacobus Johannes Wilhelmus Hammer
Father Theodorus Roelf Hammer.
Mother Cornelia Geertruida Lelie
But then again:
10th November 1869 birth for Fredrik Hendrik Hammer
Father Theodorus Roelf Hammer
Mother Cornelia Geertruida Lelie
So this could be his parents and siblings?
Can't spot an obvious birth record for a Theodore?
EDIT: I did find this however?
14th May 1863, at Herwen en Aerdt (Rijnwaarden)
Theodorus Johannes Hammer
Father: Frederick Henderick Hammer
Mother: Henrica Catherina Lelie
But the town is very close to the German border?