"For which great nation has God as close to them, as is Hashem our God whenever we call upon Him?
And which great nation has statutes and laws, as righteous as all the law which I present to you today? (4:5-6)
In these two lines Moshe alludes to two of the main forms of religious experience - the experiential/spiritual, versus the intellectual. He says that the Jewish people has experienced both, in ways that no other nation has.
Now, it is easy to think of extraordinary spiritual experiences that Moshe could be alluding to, for example the splitting of the Red Sea. It is also easy to think of intellectual experiences, specifically the many laws which Moshe taught them over the course of 40 years. But there was only one event which was a spiritual and an intellectual experience. This was the revelation at Sinai. It should be no surprise that Moshe now mentions Sinai as the lasting evidence for the claims he has just made...
Only beware, and watch yourself carefully, lest you forget the things which your eyes saw, and lest they leave your heart all the days of your life; but rather make them known to your children and grandchildren - the day you stood before Hashem your God in Horev..." (4:7-10)