Yes. The French Revolutionary calendar or the Jacobin Calendar was an attempt to do such a thing.

The Convention of October 1793 proclaimed the calendar in the spirit of anticlericalism that was sweeping France at the time of the Revolution. The Jacobin or Republican era was proclaimed to have begun on the autumnal equinox of 1792.

The year was divided into 12 months of 30 days each. At the end of the year (with years beginning and ending on the autumnal equinox), there would be five or six days called the Sans-culottides, a series of national holidays. Each holiday was dedicated to a different spirit ─ the spirit of Genius, the spirit of Labor, the spirit of Noble Actions, the spirit of Awards, and the spirit of Opinion. The sixth, in leap years, was dedicated to the Revolution and was supposed to be a grand celebration.

The names of the months were changed:

• Vendémiaire - something to do with wine/grapes

• Brumaire - fog/mist

• Frimaire - frost

• Nivôse - snow

• Pluviôse - rain

• Ventôse - wind

• Germinal - seed

• Floréal - blossom

• Prairial - meadow

• Messidor - harvest

• Thermidor - heat

• Fructidor - fruit

Each month's 30 days were divided into 10-day decades, and each day had the name of something related to its theme month. In Vendémiaire, for example, each day was named after a food or flower (except each 5th or 10th day, which was named after an animal or tool).

The Jacobin calendar fell out of use in the later Napoleonic period for a variety of reasons, not least of which was that working men liked to have a weekend every seven days, not every 10.

A couple things to unpack here.

First of all, there are a great variety of calendar systems across the planet and historically, some of which don't use specifically religious starting dates. For instance, imperial era systems in east Asia (China, Korea, and Japan) which named eras for sitting emperors. As an example, the Meiji period in Japan which begins at the start of the Meiji Emperor's rule and ends with his death. So 1912 (when the Emperor died) would be Meiji 45 since it was 45 years since his ascension to the throne. It is more complicated than that, and it does have a use for the Gregorian calendar in this system, but the point is that not all calendar systems have inherently religious starting dates.

One possibility (based on science, however you qualify that) is the scheme used for radiocarbon dates. Radiocarbon (C14) dates are always reported in years BP (Before Present). This is a bit of a misnomer since there is actually a fixed date involved. If you see a radiocarbon date of 3500BP this doesn't equate to the year 1485BC (AD2015 - 3500 years). "Present" in "Before Present" is actually 1950 (which is set because of the increase in atmospheric C14 after 1950 due to atomic testing and other factors), so 3500BP would actually be AD1950 - 3500 years, or 1550BC in the Gregorian calendar.

All that said, radiocarbon dates are never precise to a single year (you should always include an error of +/- years), so this really doesn't operate as a standard year-by-year calendar.

Second issue is that it would be exceedingly difficult to reach any consensus on what date would be a suitable starting date for a calendar intending to represent the entire human population.

Take for example 1775 (or whenever you choose in the 18th century). While you could argue exactly as your professor did, you need to bring in the spatial component. When you talk about the rise of bourgeoisie, is that really applicable in Papua New Guinea or in Hawaii? Any of those metrics you mentioned (with the exception of world population reaching 1 billion) are really quite particular to parts of Europe and not representative of the historical experience of the entire human population. This is the difficulty of choosing a single date, picking something that represents something significant to the entire planet at that point in time. If you pick 1775 (or whatever other date you choose) based on the criteria you mentioned it really isn't that much different than using a Gregorian calendar based on a Christian starting date to represent non-Christian populations. You just exchange a date based on what is significant to Christians for a date that is significant to only some percentage of the human population at that time.

We can also go down the rabbit hole of arguing what is or is not "significant" in historical terms.

Along those lines, I'm not terribly convinced that a calendar based on "science" (whatever that would look like) would be any more representative of all of humanity than one based on a particular religion. "Science" as a formal discipline is a social and cultural phenomena (just like religion and everything else we humans do) that is very particular to the present and recent past.

In other words, a scientific calendar (or one put together by historians) is not necessarily more objective or all-inclusive than a calendar based on some religiously significant starting date. At the end of the day, the criteria by which you judge the "significance" of a historical moment as used for the purpose of constructing calendars is very specific to the historical moment in which that calendar is being formulated, and so trying to create a universal calendar is pretty doomed to failure.

Has anyone? Sure! there was a lively discussion on this question in the sub ages ago; you can check out everyone's creative suggestions

• If you were to make an alternative to BC/AD, what point in history would you start with for year 1? What's the first human milestone that you can accurately date?

and a related thread here

• Do any historians use the Holocene Era calendar in their work? (current year = 12013 HE)