I'd put it between the earliest start date being 1650 and the latest 1700.
So far they have revealed the Exploration Tech Tree only to the next to last set of techs, one of which is 'Gunpowder'. The units available from that Tech are a Galleon, a Bombard-type cannon and a 'Musketman'(identifications by
@AriochIV on his Well-of-Souls site).
The dates for the first appearance of the Bombard are roughly 1360 - 1375.
First appearance of the gun-armed Galleon: 1530 - 1560
First arquebus or musket as an individual weapon: 1425 - 1475, with the Tercio formed by 1530.
Now, there is one more 'tier' of Technologies before the end of the Age, but this 5th Tier basically dates itself by the units available to about 1360 - 1560. Allow another 200 years for the sixth Exploration Age tier of tech, and we are at 1760 - the start of the 'take-off' for Industrialization in England (effective Steam power is just 15 years way with Watt's developments of 1775 - 1776).
The major Unknown is how much time/years/turns they plan for the Crisis Periods at the end of each Age, but I suggest that Modern Age is not designed to start before the end of the 18th century, and the Napoleonic Wars, rise of rampant (European) Nationalism, and start of the social and ideological discord raised by Industrialization may all be part of the Crisis that leads into the Modern Age.
As for the Holy Roman Empire, as I've posted before, if there is a massive campaign to include it, I would put it in a 'special category' of entity which you may form in-game, not receive as a choice by starting a new Age. It is, after all, almost everything the traditional 'Civ' is not: it is wildly discordant and disconnected as to ethnicity, identity, language and space, it was, at best, a set of political compromises from start to finish, and its military power frequently relied on the cooperation of mutually hostile internal states and polities. Other Civs in the game have some of those problems, but I don't know of any that had all of them, all the time. It deserves to be handled differently, and leave its components like Austria, Bavaria, Prussia and Saxony a separate existence.