Born on August 9, 1878, in Bay View, Maryland, Welsh attended the country schools and the public schools of Philadelphia, Pennsylvania.[1] He took business and academic courses from Temple University and engaged as a legislative stenographer and reporter from 1895 to 1901.[1] He received a Bachelor of Laws in 1905 from Philadelphia Law School of Temple College (now Temple University Beasley School of Law) and was admitted to the bar the same year.[2] He entered private practice in Philadelphia, Pennsylvania from 1905 to 1923.[2] He was Secretary to Mayor John Weaver of Philadelphia from 1905 to 1906.[3] He was an assistant city solicitor for Philadelphia from 1906 to 1907.[2] He was an assistant district attorney in Philadelphia from 1907 to 1922.[2] He was Secretary of Temple University from 1914 to 1938, and began serving as its first Vice President in 1938.[1] He was President of the Republican district executive committee from 1914 to 1932.[1] He attended officers' training camp at Fort Niagara, New York in 1917.[1] He was a member of the Board of Education of Philadelphia County, Pennsylvania from 1921 to 1932.[2]
Welsh married Nellie Ross Wolf of Bermuda in 1906. They had two sons, William Austin Welsh and James Conwell Welsh. In 1921, he married for the 2nd time Helen Reed Kirk and they had three children together, Margaret, Patrick and Deborah.[6]