No, if you don't have a backup of your own they are gone.
Technically messages only need to be stored on a server until they are delivered (up to some maximum time). Once that it done they are deleted. Many people would not regard it as desirable for the carrier to keep a copy of their personal communications.
In some countries the carrier may be required by law to keep the messages (or at least records of who messages were exchanged between) for some period of time after delivery in case the police or security services turn up with a warrant. But that doesn't necessarily mean that they'll release a copy of the message to the phone user even if they have it somewhere. And the records will be deleted once the statutary period expires, because storing them costs money and the company receives no benefit from doing so.
In the case of ATT they say that they keep the records of who messages were sent to/received by and when for some period, but don't store the message content at all. So in principle you could get the phone number, but 3-4 years is probably too long in the past. I've seen a message that you can log into your ATT account and look for text logs in your usage section, but that the record will only go back 16 months (I'm not an ATT customer so can't verify any of that).
