This week's parshah, Bechukotai, gives a list of blessings for following the ways of Hashem, and curses for straying from His paths. It links the curse of exile with a specific mitzvah: Shmitah. It is written as follows:
ויקרא כו:לז - אז תרצה הארץ את שבתתיה כל ימי השמה, ואתם בארץ איביכם, אז תשבת הארץ, והרצת את שבתתיה
Vayikra 26:37 - Then the land will be appeased of its sabbaticals, all the days of desolation, and you are in the land of your enemies, then the land will rest, and be appeased of its sabbaticals.
Basically, from the time of Yehoshua bin Nun (2488) until the time of the destruction of the 1st Beit HaMikdash (3338), there are 70 Shmitah's worth of sin that need atonement. One might say that the starting date is either when Yehoshua entered the land (2488), or it is really after the land fell to Yehoshua after 7 years of conquering, in the year 2495. Either way, it is slightly over 840 years total.
For explanations as to the exact substance of these 70 years, see the commentators both on this chapter of Vayikra, as well as Divrei HaYamim II, 36:21. Rashi has a detailed list in Divrei HaYamim, but also see the GR"A there.
In Daniel 9:24, we learn that the decree put upon Am Yisrael is not 70 years, but 70 weeks of years, i.e. 490 years. This is the time from the destruction of the 1st Beit HaMikdash to the destruction of the 2nd. 3338 until 3828.
If so, we can see, perhaps, that the 70 years in Galus Bavel were a tikkun for the Shmitah years before the destruction of Bayit Rishon, and the 420 years thereafter are for the other years. Violation of Shmitah brings the punishment of exile, so this punishment, of exile from the land, came first.
The period from Yehoshua until the Churban was more aligned with Chesed, with open miracles and prophecy and Jewish autonomy for a majority of the time, whereas the 2nd Beit HaMikdash was more aligned with Din. Miracles were on a more natural level (Purim is one example), prophecy came to an end, and Jewish autonomy was for but a minority of the time.