Is there a website that allows you to find what Daf was studied on the a particular date as part of the Daf Yomi cycle?
I have found that Daf Yomi Calendar has the calendar for cycles 11 - 15. This site does not have any earlier cycles.
I have found D.A.F.'s Talmud Tools which allows you to search back by Daf, Hebrew date, or English Date. The first cycle shown is Brachos 2 which started Sep 6, 1923, Thu, 25 Elul 5683 and ended Sep 11, 1923, Tue, 1 Tishrei 5684.
As an example, I was born on 9 Cheshvan 5707 (Sunday November 3, 1946) which was Pesachim daf 27 of the fourth cycle.
The Simple Luach app lists the day's daf in its calendar. Navigate to the calendar tab, and click the icon at the top right. This goes back to September 11, 1923 which lists Berachos 2 as the day's daf. The previous day, September 10, (and all earlier days) lists the day's daf as "null". Here are screenshots showing this:
TorahCalc recently added an online calculator that does exactly that. You can enter any date and it will tell you the Daf Yomi page and cycle number for that date.