How do Christians who think animals have only existed for <7,000 years on Earth reconcile their views with Pleistocene saber-toothed tigers? Saber-toothed tiger (smilodon) fossils are regularly dated to the Pleistocene (such as here), which would put them before animals existed according to many Christians (at the earliest, ~12,000 years ago).
How do Christians who reject animals existing &gt;7,000 years ago reconcile their views with the Pleistocene-existing saber-toothed tigers, according to scientific sources?
I think your premise may be flawed.
You ask about &quot;Christians who reject animals existing &gt;7,000 years ago&quot;, but that implies Young Earth Creationists, who reject anything (other than God, of course) existing more than 7,000 years ago.
This means that they also reject any dating of any worldly substance (at least on Earth, but that's a whole other can of worms) which claims an age of more than 7,000 years. So there is no &quot;reconciling&quot; to be done; the Christians you are asking about reject your implied premise.
If you are genuinely curious to learn more, here are a couple places you can go that will start to give you some information on the basis of YEC rejection of Uniformitarian dating:
https://creation.com/how-old-is-the-earth
https://answersingenesis.org/age-of-the-earth/

If you want something with a little more meat, I cannot recommend strongly enough that you read the R.A.T.E. report. You can read a summary here, or download the full report here (fair warning: this is a book; 686 pages long). The second report may also be available. (Personally, I own both in physical form.)