The first date is always more recent than the second
Sounds just fine, if you're sure it's true! (It is in this case, of course). In this type of situation, when you're looking for an adjective (comparative) to use, my advice is use the one most suited to the noun (thing) you're describing.
On face value, those are numbers in your example. But really, they're dates. Dates = time, so we need adjectives to refer to this concept of time.
Greater is for numbers (integers, fractions, etc).
You could explore avoiding an adjective altogether, for example:
The first date always comes before the second
Or, switching your order:
The second date always comes after the first. @JR