Did we simply not know where it was? Or did we lack the technology to seek it out? Did people ever excavate shipwrecks before modern times? If we knew where the Titanic was even fifteen years after it sank, how might we have gone about excavating it?
It is always easier to explain why an event occurred when it did than to explain why it did not happen earlier. In the case of the Titanic wreck, it was in the realm of possibility that the ship could have been discovered earlier than 1985. There were some attempts to find the ship, but they did not pan out until Robert Ballard's expedition. The discovery of the Titanic involved several interlocking factors that came together in 1985,
Part of the problem with finding a wreck on the open ocean is that the ocean is, to paraphrase the British writer Douglas Adams, is big. Really big. Even though the Titanic was a very large ship, it is a speck compared to the rest of the Atlantic Ocean, or even the general region of her last reported location. Added to this problem, the Titanic was in a fairly deep part of the Atlantic. This XKCD comic imparts some idea of where the wreck lies in relation to other parts of the world. This all meant was that the main wrecksite was around twelve miles away from her last reported position. These positions may have been inaccurate, or the wreck may have drifted considerable distance on its way to the bottom, or some combination of both factors. But whatever the case, any would-be discoverer of the Titanic was going to be starting in the wrong place and having to look into the ocean depths.
The depth of the wreck was a major obstacle. The exploration of the ocean depths beyond a thousand feet began in the 1930s with bathyspheres, which were towed steel balls that could withstand the intense pressures of the ocean depths. The first generation of bathyspheres were very rudimentary and there were a lot of unknowns involved in these first steps into the deep. Oxygen mixtures, pressure limits, and other operational factors were still being felt out by these adventurers.
Deep-sea exploration technology matured over the course of the two decades after the 1930s bathyspheres. The Trieste, described here by one of its crewman, managed to get to the bottom of the Marianas Trench in 1960. There were other deep-sea explorations on the 1960s and the era did see a number of firsts for deep-water explorations.
This raises the question of then why was the Titanic not found in 1965 instead of 1985. The answer is partly due to while the technology existed to reach these depths by 1960, the technology did not really exist yet to find the wreck. Unless you knew exactly where the wreck was, vessels like the Trieste, or follow-ups like Alvin- described here- could not find it. There were limits for surface-based sonar as to how clear of an image of the bottom it could receive. The development and maturation of side-scan sonars in the 1960s promised to solve some of the problem. But this actually proved chimerical for the French National Institute of Oceanography (IFREMER)'s attempt to find the Titanic alongside Ballard's expedition. Ballard described the IFREMER's side-scanning sonar sweeps as "mowing the lawn" as they were covering a search-box systematically and slowly.
IFREMER's expedition did assist Ballard in that they showed him where not to look, but the solution Ballard used to find the Titanic was somewhat low-tech. The Acoustically Navigated Geological Underwater Survey (ANGUS) was a towed camera system that could visually survey the ocean floor. ANGUS had already been proven in its exploration of the Mid-Atlantic Ridge in Project TIMELESS in 1975. The technique Ballard and his team used was to use the ANGUS array to visually scout for the debris field. Counter-intuitively, this was a much more productive way to find a wreck like the Titanic's which, unbeknownst to pre-1985 explorers, had broken up. This created a large debris field that while it did not create much of a sonar return could be sighted visually. Although scanning with the ANGUS can aptly be described as "looking at mud, and more mud," exploring the regions IFREMER and Jack Grimm's 1981 expedition had not gone over raised the chances of ANGUS's success.
Ballard had another asset available to him when searching for Titanic: experience. These expeditions were expensive and time-consuming. Although the Woods Hole Oceanographic Institution could foot part of the bill, they did not cover all the bases. The Ballard expedition though had a silent benefactor though that was not publicized in the 1985 media hoopla, the US Navy. Ballard had actually pioneered his debris-spotting technique as a means to locate two sunken US Navy submarines, the USS Thresher and the USS Scorpion. Woods Hole's expedition for the Titanic was actually a cover for finding these submarines and the USN underwrote improvements into the ANGUS (ARGO) and a remote-operated vehicle for Alvin , the Jason Junior. The expedition to find the submarines allowed Ballard and company to recognize that the debris pattern for deep-water wrecks was different than shallow-water wrecks with the former forming a trail of debris. Ballard had actually worked out a side-deal with the USN that after he had mapped the submarines, he would be free to search for the Titanic. The USN agreed and the Ballard had three weeks of searching that the USN had budgeted for the total expedition.
The success of Ballard's expedition in 1985 was not just happenstance, but the result of maturing technology coupled with an experienced team that possessed a financial backer with deep pockets. There had been other expeditions to find the ship, most famously the Grimm one which claimed to have found one of the propellers- see this discussion on encyclopedia-titanica for more information- but came up short. The technology used to discover the Titanic had matured by the 1970s to be able to discover the ship, but it was a process that required an investment of time to find it. The tools used to reach the wreck once it was found were actually older than the ones used to discover it, which underscores the difficulties of finding a needle in a vast Atlantic haystack.