Efficient way to find matching date ranges?
Your question is not clear.

I am assuming you have 1000 date intervals in some set $A$ and another 1000 in set $B$ and you wish to find which intervals in $B$ lie completely inside some interval in $A$.

For an interval [x,y] in $B$, search points $x$ and $y$ in the segment tree built on $A$ and find sets that overlap.

Look up Segment tree.

Its stores line segments with starting point and end point.
You can modify it to store start date and end date.

https://en.wikipedia.org/wiki/Segment_tree