Looking on the internet deeply has found these results:

No surprise is the most popular phrase on the web.

Not surprisingly 115,100,000 results on the web	No surprise 135,200,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
Not surprisingly check along with your family members doctor before attempting any prescription based hair loss treatment. Not surprisingly, evidence suggests that 5HTP may be effective as well. Not surprisingly, careful and sophisticated plans were developed about how to organize the world. Not surprisingly, Pope Pius was the only one to see this vision. Not surprisingly the public gave President Carter low marks for his handling of the economy. Not surprisingly, some Christians weren't amused. Not surprisingly, the Commission's FMD proposal has prompted vigorous debate amongst all interested parties. Not surprisingly, this destruction also endangers bonobo survival.	It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

Not surprisingly

115,100,000 results on the web

No surprise

135,200,000 results on the web

More popular!

Not surprisingly check along with your family members doctor before attempting any prescription based hair loss treatment.
Not surprisingly, evidence suggests that 5HTP may be effective as well.
Not surprisingly, careful and sophisticated plans were developed about how to organize the world.
Not surprisingly, Pope Pius was the only one to see this vision.
Not surprisingly the public gave President Carter low marks for his handling of the economy.
Not surprisingly, some Christians weren't amused.
Not surprisingly, the Commission's FMD proposal has prompted vigorous debate amongst all interested parties.
Not surprisingly, this destruction also endangers bonobo survival.

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.