There were sects of Judaism that believed that the morning began the day of the Jewish calendar. i am not familiar with how the Sadduccees did their calendar, as they did not survive as a sect, nor did any of their writings (if they had any). Many people equate Sadduccees with Karaites, but this is not correct, Karaites follow the normal Jewish calendar, with exceptions to how a new moon is reckoned, and when Shavu'ot is.
If indeed the Jews at Qumran were Essenes, then we could say that there was an Essene calendar that was based off the book 1 Enoch and Jubilees. While you might not find the very specific phrasing of "the day begins at sunrise," the calendars they propose are solar calendars, which have their basis with the rising and the falling of the sun as their measurement of counting days. Unlike a lunar calendar, which is based on the appearance of (or lack thereof) the moon. Many ancient civilizations used a solar calendar, and in fact a variant of a solar calendar is what is commonly used in America, given to us by the Romans, which is why we reckon the day at sunrise. So when you read discussions of ancient Jewish sects, the term solar calendar has the implicit understanding that the days are reckoned at sunrise.
You can read some information regarding the calendar of Enoch here. Be aware that if you do a Google search of the Enoch calendar you will find lots of websites of new "Messianic Christian" sects that are attempting to revive the use of the Enochian calendar.
In terms of normative Judaism, the Rashbam claims that the Jewish day begins at sunrise, though he also says that his words are not to contradict halachah, but that he is simply giving what he considers the p'shat of the text. It is unknown if he was aware of any Essene documentation or if he came to this conclusion on his own.
Rashbam on Genesis 1:5
ויהי ערב ויהי בקר – אין כתיב כאן ויהי לילה ויהי יום אלא ויהי ערב, שהעריב יום ראשון ושיקע האור, ויהי בוקר, בוקרו של לילה, שעלה עמוד השחר. הרי הושלם יום א’ מן הו’ ימים שאמר הק’ בי’ הדברות, ואח”כ התחיל יום שיני, ויאמר אלהים יהי רקיע. ולא בא הכתוב לומר שהערב והבקר יום אחד הם, כי לא הצרכנו לפרש אלא היאך היו ששה ימים, שהבקיר יום ונגמרה הלילה, הרי נגמר יום אחד והתחיל יום שיני:
And it was evening and it was morning – It does not say “it was night
and it was day”, but “it was evening”, [meaning] the first day passed
and the light set, “and it was morning”, the ending of the night, for
the dawn broke. One day of the six days mentioned in the Ten
Commandments was completed. Afterwards the second day began, and God
said “Let there be sky.” The verse is not coming to tell us that
evening and morning constitute one day, for we do not need to explain
anything but how the six days were, for with the coming of the morning
the night was over – thus one day was completed and the second day