I am assuming a theocratic state as a matter of religious dogma is eternal. It has no beginning and no end. It has always been and always will be. In reality of course history has simply been rewritten to omit or distort anything that might imply that there was a time the empire did not exist.
The founders of the empire were intelligent enough to realize the empire must be capable of adapting to changes and in order to do that people must be able to learn from the past. So study of history can't be outright banned or even restricted to a closed inner circle.
Neither is it really practical to hide the fact other governments with different systems have existed. Such alternate systems would be too valuable as sources of wider perspective on many issues.
So what is hidden is the wider framework that could be used to compose long timelines and notice the imperial timeline starts after some other timelines.
Essentially for time a modulus calendar is used. Say this year would be the 15th year of the current century. But there would be a number given for the century and no concept of millennia, other than noting that since the empire is eternal it must have existed for countless millennia. People might also talk of events of the previous century. So George Orwell wrote a book about the 84th year of the previous century. Also allowed would be speculation and expectation of the next century. So there would be sliding time window of few hundred years as the maximum length of historical context.
Geographical context would be similarly localized. A scholar might note that the heretical kingdom he is studying has familiar features, but only the most radical heretic would even suspect the kingdom was located at the location of the Imperial Capital. And even he would simply assume there was another capital at the time, not that the kingdom existed before the empire.
I doubt there would be major issues from this as rulers generally fail to learn from history anyway, but just in case:
How would this limit the study of history and the development of related sciences? Would there be some practical issues? Would there really be practical benefits over simply banning the study of history?
Edit based on answers (or some stuff I clearly should have mentioned):
The eternal empire has no particular desire to make itself look better than it is or its alternatives worse beyond what comes naturally from self-censorship. It is eternal. Resistance is futile. So the powers that be, are actually more concerned about having access to accurate information they can use to secure the future than looking good. As a theocratic state the nominal head of state is probably the national divinity anyway. People are welcome to go complain to him, if they think the government is messing up.
Actually, a big part of what I'd like to know, if this kind of selective "tolerance" based on the government itself believing itself to be eternal and God ordained would be practical given that things contradicting the dogmatic stance on the empire being eternal are hidden. That is the context for the third question concerning practical benefits above.
Leushenko reminds of the vast difference between eternal and long lasting. Quoting my comment to his answer since it explains why the empire values study of history and does not ban it or outright falsify history. I thought that just stating they do in the question would be enough, but in retrospect that was simply wrong.
Yes, the question assumes this difference between eternal and merely ancient. Being eternal does not imply being cyclical unless you also assume reality to be finite in some way. The empire rejects the idea of God's creation being limited in a way meaningful to mortals as heresy. I imagine their view of time would be an infinitely ascending spiral that goes through same general pattern but never repeats. So you could learn from the past, but not repeat it. As matter of dogma they'd continually face entirely new events that resemble past events. That is why they would value study of history.