The first key point, is that nothing has overwritten them, in other words, other texts, pictures, contacts, and other files haven't been written to the location where they were (most OS algorithms try to use your devices' memory in such a way that this is typically the case, the memory is used in a queue, to maximize longevity).
The second part, and where it gets fairly intensive, is using either an Android recovery app (somewhat useful, less-so without admin access), or using something like the Android Debug Bridge, to read the device from a PC, and do essentially the same thing (but the PC has a bit of a better chance, for a number of reasons).
Both methods are fairly technically involved though, and time-consuming. You don't typically end up with a "set of conversations", but more a set of files with "chunks of conversations", that you'd then piece back together.
There are probably services (definitely for PC/server market) that do it as well, for a price.
Basically, it all comes down to how important the data might be...
*If this (or another post in this thread) fixes your problem/issue, please mark it as "accept-solution", and I'll tag it, to make it easier for others to find the answer(s). FYI: I'm an AT&T end-user, just like most of us in the forum. Thanks.
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