I have not yet found a birth record for him, but have included his marriage record and the birth records of his children. His marriage records gives his parents' names as Leonhard and Catharina Poelstner, and also names his wife's parents, Michael and Anna Trump.
Marriage Record
Name Michael Poelstner
Birthplace Erzberg, Bayern, Germany
Spouse's Name Maria Trump
Spouse's Birthplace Gailroth, Bayern, Germany
Event Date 02 May 1676
Event Place Michelbach A.D.L., Wuerttemberg, Germany
Father's Name Leonhard Poelstner
Mother's Name Catharina ...
Spouse's Father's Name Michel Trump
Spouse's Mother's Name Anna ...
Marital Status Single
Spouse's Marital Status Single
Children
Name Georg Matthias Poelstner
Event Date 1678
Gender Male
Birth Date 20 Apr 1678
Birth Year 1678
Birthplace Gailroth, Bayern, Germany
Father's Name Michael Poelstner
Mother's Name Maria Trump
Paternal Grandfather's Name Leonhard Poelstner
Paternal Grandmother's Name Catharina ...
Maternal Grandfather's Name Michael Trump
Maternal Grandmother's Name Anna ...
The next two boys were twins.
Name Georg Poelstner
Event Date 1679
Gender Male
Birth Date 06 Jul 1679
Birth Year 1679
Birthplace Gailroth, Bayern, Germany
Father's Name Michael Poelstner
Mother's Name Maria Trump
Paternal Grandfather's Name Leonhard Poelstner
Paternal Grandmother's Name Catharina ...
Maternal Grandfather's Name Michael Trump
Maternal Grandmother's Name Anna ...
Name Michael Poelstner
Event Date 1679
Gender Male
Birth Date 06 Jul 1679
Birth Year 1679
Birthplace Gailroth, Bayern, Germany
Father's Name Michael Poelstner
Mother's Name Maria Trump
Paternal Grandfather's Name Leonhard Poelstner
Paternal Grandmother's Name Catharina ...
Maternal Grandfather's Name Michael Trump
Maternal Grandmother's Name Anna ...
I could not find a birth record for his daughter Maria, but a copy of her death record also gives her birth year and place, and confirms the names of her husband and parents.
Name Maria Poelstner
Gender Female
Death Date 08 Dec 1744
Death Place Michelbach A.D.L., Wuerttemberg, Germany
Age 62
Birth Date 1682
Birthplace Gailroth, Bayern, Germany
Marital Status Widowed
Spouse's Name Georg Reissig
Father's Name Michael Poelstner
Mother's Name Maria Trump
Michael Poelstner is also listed in the marriage record of his daughter Maria to Georg Reissig.
Name* Georg Reissig
Birthplace Triftshausen, Wuerttemberg, Germany
Spouse's Name Maria Poelstner
Spouse's Birthplace Gailroth, Bayern, Germany
Event Date 08 Jan 1700
Event Place Michelbach A.D.L., Wuerttemberg, Germany
Father's Name ... ...
Mother's Name ... ...
Spouse's Father's Name Michael Poelstner
Spouse's Mother's Name Maria Trump
Marital Status Single
Spouse's Marital Status Single
Sources
"Deutschland Heiraten, 1558-1929," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:J4VJ-NDB : 26 December 2014), Michael Poelstner and Maria Trump, 02 May 1676; citing Michelbach A.D.L., Wuerttemberg, Germany; FHL microfilm 1,528,594.
"Deutschland Geburten und Taufen, 1558-1898," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:NCJ6-P81 : 28 November 2014), Michael Poelstner in entry for Georg Matthias Poelstner, ; citing Gailroth, Bayern, Germany; FHL microfilm 1,528,594.
"Deutschland Geburten und Taufen, 1558-1898," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:NCJ6-KVB : 28 November 2014), Michael Poelstner in entry for Georg Poelstner, ; citing Gailroth, Bayern, Germany; FHL microfilm 1,528,594.
"Deutschland Geburten und Taufen, 1558-1898," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:NCJ6-P81 : 28 November 2014), Michael Poelstner in entry for Georg Matthias Poelstner, ; citing Gailroth, Bayern, Germany; FHL microfilm 1,528,594.
"Deutschland Geburten und Taufen, 1558-1898," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:N5PT-RYQ : 28 November 2014), Michael Poelstner in entry for Michael Poelstner, ; citing Gailroth, Bayern, Germany; FHL microfilm 1,528,594.
"Deutschland Heiraten, 1558-1929," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:J4VJ-69H : 26 December 2014), Michael Poelstner in entry for Georg Reissig and Maria Poelstner, 08 Jan 1700; citing Michelbach A.D.L., Wuerttemberg, Germany; FHL microfilm 1,528,594.
"Deutschland Tote und Beerdigungen, 1582-1958," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:J449-KWR : 28 November 2014), Michael Poelstner in entry for Maria Poelstner, ; citing , reference ; FHL microfilm 1,528,593.
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