↑ Lincolnshire Pedigrees both identifies him as the 1st son and gives his baptismal date as Feb 1592/93. The baptismal dates given for this family are too close together to reflect actual birth dates. In fact, in order to make the order of the sons match this source, it is necessary to place William's birth before 1592, and preferably before 1590. Another source says William was born Oct 1583, with no suggestion that that William died and another was born later.
Therefore, I propose that the William born Oct 1583 is the son identified as the 1st son in the Lincolnshire Pedigree. It is possible that the author got his baptismal date wrong and it should be Feb 1583/4, or that he was baptized at the age of 9 (I couldn't locate a baptismal record for him in FamilySearch). Either way, he couldn't have been born in Feb 1592/3 if Benjamin was born in Jul 1593.