Bielaski was born in Poland, and in 1831 took part in the armed rebellion against the Russian Empire known as the November Uprising. After the failure of the rebellion, he was exiled to France, later immigrating to the United States. In 1837 he became an engineer in Illinois, where he got married and became acquainted with Abraham Lincoln. Bielaski moved to Washington, D.C. to work for the General Land Office, working his way to principal draftsman in 1853.