1). The calendar system is accepted as a tradition and so presumably is the "calendar" system that was used before Hashem turned over the calendar to Chazal to mkadesh.
2). According to the Avudraham this is the correct system for determining leap years at all times. (I need a source, quickly skimmed and couldn't find it, I never read it, but heard it in his name).
3). We make Birkat HaChama when the sun returns to its "original" location during creation. Though this might just mean the specific hour on Tuesday I am sure there are opinions who are more astronomically minded. If so, it presumes a 19 year cycle from creation - otherwise there would be drift.
4). Molad is calculated based off of the previous new moon... so even if the first molad was given as Nissan in Egypt, you can just work backwards.
5). To know the exact millisecond would likely be impossible no matter what system since there were events like Hashem stopping the sun for Yehoshua. Unless you believe all these acts balanced out perfectly (like perhaps setting quicker by Yaakov). I can see this as a matter of debate.
Your question seems to depend on adding two Adars. If Chazal added an "extra" month too many, they would need to remove a month in the future otherwise things would not be balanced. So things would even out. At best, it could be a "month" off, giving you a few possibilities.
Similarly the Gemara (Rosh Hashana (10b)) has a Machlokes if the world was created in Tishrei/Nissan and when the Avos were born etc... This imo presumes that the calendar was operative otherwise I don't particularly understand the machlokes. It would imo mean our Nissan and Tishrei. To disagree, one would need to argue, that the date doesn't matter, but the metaphysical month, which I suppose is possible.
In a different point, the Ramban points out that Tishrei overlaps with the symbol of the weights/measure in astrology. Something that was passed down even among non-Jews, that this is a time of judgement. It would appear that Tishrei was always at this time. (Drasha Rosh Hashana)
In a similar vein that the Chafetz Chaim (Shem Olam Chelek Aleph Perek Gimmel) (and Ramban above) points out that the Sheep/Goat/Ram is the month of Nissan at the time when the Egyptians worshiped their deity. At that time we took their idol and slaughtered it in its month when the moon was full (precisely chazot).
Now perhaps you could argue that it happened that hebrew year just "happened" to realign with the summer (non-Jewish) and astrological calendar. I suppose this is possible, but not once again Pashut Pshat.
It would appear to me that the Calendar existed with leap months.