Autumn quarter here starts in the last week of September. Bambi was born on August 4th. That gives mama Obama about a month and a half from the time of his birth to move to Seattle and attend classes.
I don't see why anyone would find that implausible.
The issue is that Stanley Ann's transcript, both in the "filled in by typing" and computer printed versions, say that she started on in late September, but rather August 19th. It could be that both are in error, but this seems unlikely. The date was typed twice on that record, and both of the dates are definitely "8-19-61" while the computer version says 08-19-61, also twice, and the image of that is quite clear.
IF that date is correct, that gave her 15 days. An anecdotal report from one of her friends puts her in the area not latter than late August, with Barry in tow, and AFAIK, that anecdote was reported well before the transcripts surfaced.