A more succinct expression for "The day before yesterday"

Solution 1:

The words you are looking for exist in English, but they have been abandoned and are only found in old texts.

1535, Coverdale, Bible, Genesis 31:2
And Iacob behelde Labans countenaunce,   And Jacob beheld Laban’s countenance,
& beholde, it was not towarde him as     and behold, it was not toward him as
yesterday and ereyesterday.              yesterday and ereyesterday.¹

1535, Myles Coverdale, The Byble, that is, the Holy Scrypture of the Olde and New Teſtament, faythfully tranſlated into Englyſhe, Tobit 8:4, page D.iiij
Thē ſpake Tobias unto the virgin, and    Then spake Tobias unto the virgin, and
ſayde: Up Sara, let us make oure         said: Up Sarah, let us make our
prayer unto God to daye, tomorow, and    prayer unto God today, tomorrow, and
ouermorow: for theſe thre nightes wil    overmorrow: for these three nights will
we reconcyle oure ſelues with God: and   we reconcile ourselves with God: and
whan the thirde holy night is paſt, we   when the third holy night is past, we
ſhall ioyne together in ye deutye of     shall join together in the duty of
mariage.                                 marriage.²

Note how closely these words are related to the German you ask about, because these languages have a common ancestor. Consider these sister terms:

• over- and über- “from Proto-Germanic *uberi”³
• yester- and gestern “from Proto-Germanic *gestra-”⁴
• morrow⁵ and morgen “from Proto-Germanic *murgana- ‘morning’”⁶

Solution 2:

From the past to the future:

   -2 days                         -1 day               +1 day                +2 days  
   ereyesterday or nudiustertian   yesterday    today   tomorrow (or morrow)  overmorrow

The fact that they are not all in current usage does not mean they will not revamp sooner or later.