Thanks EileenWilson001 for that information, which is what I have. So the questions I have remain:
1) Who was Mollie Goldberg? On the Petition For Naturalization, there is no indication of what name she came over from Europe as - no maiden surname or 'real' first name. Her petition also omits under the Act of Sept 22, 1922 Declaration of intention Number or certificate of arrival.
2) Mollie Goldberg apparently does not have her name listed on a passenger list under that name. He came through Rotterdam, Holland and gain entry into NY on Jan 15, 1904. So what real name did she use?
3) If both David and Mollie immigrated in 1904 and had their first child in 1908, the assumption of their marriage is between those dates.
4) Notice that Bella and Jacob "appear" on the 1915 census but not on the 1910 census. That's because they came over in 1911 and where born to David Goldberg when he used the name David Melamed to gain entry into the US and had Bella and Jacob with Rose Braunfeld (also Austrian).