There are no hack to get get to the very beginning of a text thread when it spans over a long time. You can Tap on the top section of the message thread and it will move down a page at a time. Try that as well.
The other thing to do is to launch the Messages app and while you are in Names list you can Pull Down from the center of that screen which will reveal the Search bar at the top. You can then search for w word or a phrase that you may have used during the course of the texting relationship and hope that the results will reveal the time frame that you interested in looking for.
I know that none of the above resolves your issue however I thought that I'd mention regardless. Furthermore, if you want to suggest this feature to Apple then please leave feedback here ➔ Product Feedback - Apple
Axel F.