Prior to October 1968, the Supreme Court did not regularly commission transcripts, except when the Court deemed it appropriate. For example, all the oral arguments in Brown v. Board of Education (I) and Brown v. Board of Education (II) were transcribed.
In even older cases, you’ll occasionally find transcripts of arguments recorded in U.S. Reports. Norman v. Baltimore & Ohio R. Co. is one such case. It records the “arguments” of the attorneys for both Norman and the Baltimore & Ohio Railroad Company, as well as the “oral argument” of Attorney General Cummings, along with the following footnote:
Mr. Cummings’ address, stenographically reported, has been printed in full by the Government Printing Office. Omissions from the present report are marked by dots. He also closed the argument in all of the cases.
The U.S. Reports volume makes clear that the “arguments” were simply extracted from the briefs, whereas the “oral argument” was more like a conventional transcript – except that it was edited, which severely compromises it as a record. Fortunately, a transcript “printed in full” presumably exists somewhere, and we can hope that someday all such “stenographically reported” documents will become available online.
All oral arguments in the U.S. Supreme Court cases from the 1955 Term onward were recorded by the Court on reel-to-reel tape, which The Oyez Project finished digitizing and transcribing several years ago, so with only a few exceptions (i.e., where the recording was lost, damaged, or incomplete), “unofficial” transcripts can be obtained from their website for all cases argued since October 1955.