This is an old question, but it seems that since the previous answer was written, Ancestry has made more digitized records available. There are baptism, marriage, and some death records available for the region you're interested in.
You'll need to brush up on your Kurrent (19th-century German cursive handwriting) paleography or find someone who can read it for you. You'll also want to familiarize yourself with German number and date formats ([one] thousand eight hundred seven and seventy, for example). Also, simple words like Sohn, Tochter, geboren, wohnhaft, as well as more specialized words that might appear on these official documents.
Ancestry has a marriage record for the following couple:
- (word) (word) Friedrich Gustav Tesche, ... geboren am dreizehnten Juli des Jahres tausend achthundert sieben und siebzig [born on 13th July 1877] zu Wahlsdorf, (word) Jüterbog-Luckenwalde, wohnhaft in Berlin ... Sohn der L_(?) Friedrich Tesche und (word) (word) Friederika (name?) Kutscher, (word) wohnhaft in Wahlsdorf
- Paula Margareta Golecki, ... geboren am sechs und zwanzig ten November des Jahres tausend achthundert zwei und achtzig [born on 26th November 1882] zu Berlin, wohnhaft in Berlin ... Tochter der (word) Franz Alexander Golecki und (word) (word) Elizabeth Harmina(?) Karolina geboren Newjahn, (word) wohnhaft in Berlin
There's quite a lot more detail on the marriage record. I just wrote what I could read at first glance, and I've probably mistranscribed something so you'll want to examine the documents closely.
Ancestry has baptismal records for Paula Margarethe Golecki (parents Franz Alexander Golecki and Elisabeth Hermine Caroline Golecki), 26 Nov 1882 Berlin and Julia Wilhelmina Hiltrud Tesche (parents Friedrich Gustav Tesche and Paula Margarete Tesche), 28 Oct 1905 Berlin.
Ancestry also has a marriage record for a Friedrich Wilhelm Tesche to Johanne Friederike Kutscher, 8 Jul 1876 in Brandenburg state.
If these are your people and you haven't already found these records in the past 3.5 years, you might give it another try.
You'll want to remember the FAN club principle: friends/family, associates, neighbors. So any children/siblings/parents you find, you'll want to follow both forward and backward, to find siblings/cousins because those records might mention the people you're looking for.
You say you know your Gustav's sisters' names, so try to find their marriage records, which might list the parents and the sisters' birth dates. If you think they're the right ones, try to find their baptismal records, which will support or provide more information.
- Ancestry.com. Berlin, Germany, Marriages, 1874-1920 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2014.
Original data: Heiratsregister der Berliner Standesämter 1874 - 1920. Digital images. Landesarchiv, Berlin, Deutschland.
Register Year or Type: 1904 (Zurückgeführtes Erstregister)
- Ancestry.com. Berlin, Germany, Births, 1874-1906 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2014.
Original data: Geburtenregister der Berliner Standesämter (Bestände P Rep. 100 bis P Rep. 840) 1874–1906. Digital images. Landesarchiv Berlin, Germany.
Landesarchiv Berlin; Berlin, Deutschland; Personenstandsregister Geburtsregister; Laufendenummer: 385 (Margarethe) and Laufendenummer: 920 (Hiltrud)
- Ancestry.com. Teltow-Fläming, Germany, Marriages, 1874-1923 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2016.
Original data: Ehebücher, 1874-1923. Gemeindearchiv Blankenfelde Mahlow, Blankenfelde Mahlow, Deutschland.
Ehebücher und Namensverzeichnisse, 1874-1923. Archiv des Landkreises Teltow-Fläming, Luckenwalde, Deutschland.
Year Range: 1874 - 1900