Thank you for the all guidance.
I just want to share the real experience I had because I assume this will be helpful when someone needs it.
On the first day I go for the Schengen visa, they requested DATV first. The next day I go for the DAT visa, they requested Schengen visa first. Then after few day I go for the Schengen visa again after explaining. They were very kind to understand my situation.
They accepted and I could get the Schengen visa after 10 days. Then I have applied for the DAT visa and I could get the visa after 8 working days.
So thank you very much to both consulates.
For the entire process it tooks around 7 weeks for me.