Thank You @engelchen for your response.
Thanks to @Straightpoop and @murphaph
I didn't get a notification on my email id so thought nobody has provided me a response.
Do you know how much time I have to initiate this verification process? Right now it is not started, I am working on a second option.
As I mentioned that my original documents are in India(I only have my marriage certificate original here), and there is no one at home because due to the corona situation my family moved from the city to the village (which is a safer option), so once someone will come back, I can ask them to send all these documents to me. I want to know if there is some time limit to apply for a Birth certificate for the same.
The second option, I am here in Rothenburg ob der Tauber, and before me, there were three Indian babies which were born, and they also faced similar problems.
1st case: this guy knows German, and his wife name was on his passport and wife's passport also has the name of his husband, he knows the German language very well, and he discussed with them, his marriage was also not verified, but he discussed with them and requested them to forward his application further and let it rejected from the higher authorities if there is some problem, and luckily all went fine.
2nd case: these guys don't know German, and they faced the same problem, they were asked to verify their marriage, and they submitted around 470 Euro's to start the verification, but at that time German Embassy in India was closed, and nothing happens, "Standesamt" has returned the fees, but these guys did something by which they get the birth certificate for their child.
They get their marriage certificate translated using "State Certified Translator" here in Germany, and also they contacted Indian Embassy in Munich and asked them to issue a Birth Certificate for them, and after giving these documents everything works well. And I think they get the birth certificate after 5 or 6 months.
3rd Case: these guys were in relation to the 2nd case guys, so they told everything in advance, they translated their Marriage Certificate, and get Birth Certificates from Indian Embassy Munich, and then all went well without any problem.
So, at the moment I am trying this option, and if this doesn't work I will follow the standard procedure of verification.
But let's suppose this whole process is delayed by 5-6 months, as mentioned above did I get Elterngeld and KinderGeld, from the date of birth or just from the time I get the certificate.
Also, I didn't understand this line properly.
"While you are waiting for the Urkundenüberprüfung to be completed, you can obtain an Auszug aus dem Geburtenregister that you can send to your Krankenkasse as well as to apply for Elterngeld. "
to get a temporary certificate, and apply for Elterngeld, do I need to send it to Krankenhaus.