Short answer: You should definitely use "than".
"Than" is used when making a comparison (as you are--in this case, you're comparing "sooner" to "later").
"Then" has more meanings, listed below from dictionary.com:
at that time: Prices were lower then.
immediately or soon afterward: The rain stopped and then started again.
next in order of time: We ate, then we started home.
at the same time: At first the water seemed blue, then gray.
next in order of place: Standing beside Charlie is my uncle, then my cousin, then my brother.
in addition; besides; also: I love my job, and then it pays so well.
in that case; as a consequence; in those circumstances: If you're sick, then you should stay in bed.
since that is so; as it appears; therefore: You have, then, found the mistake? You are leaving tonight then.
being; being such; existing or being at the time indicated: the then prime minister.
that time: We have not been back since then. Till then, farewell.
I hope this helps.