Baumgarten was born on 29 May 1806 in Halstenbeck, Holstein, the son of Hufner Franz Heinrich Joachim B.

He started as a farm worker in his home town but later apprenticed as a koiner in Hamburg.

He initially worked for a short time as engineer in Berling's printer and then for a few years managed P. F. Lunde's machine workshop.

The company was based in the former beer garden "Kierulffs Have" at Overgaden neden Vandet in Christianshavn.

He spent his last years on his property in Lyngby where he constructed a machine for the perforation of sheets of stamps.