There are some people and articles claiming that no such thing as an operational level of war(fare) exists. I won't link examples, for you really didn't miss anything useful if you didn't see those articles.
The question shouldn't be whether it exists. The tactical and strategic levels don't exist either. Or can you grab them? It's all made-up stuff.
The question is whether it's useful to use such levels as mental constructs, and I say yes, it is useful.
A great example is the development of European-style land warfare from1914-1940.
In 1914 land forces knew about the enormous strength of fires and about the resulting superiority of defence over offence. They just didn't develop a better answer than to bypass defensive positions, and this ceased to work when the continuous front lines reached from Switzerland to the seas.
Approaches for penetrating such defences were found by 1916 and widely known by 1917 (tanks, trained small unit manoeuvre infantry, sophisticated artillery employment), but this didn't help much at first. The army which launched an offensive was able to penetrate the defences, but its opponents were so quick at moving reserve divisions to the location by rail and foot march that all such offensives got stuck after a few kilometres.
Even the late 1917 and 1918 offensives which achieved greater successes due to war fatigue weren't satisfactory. The tactical challenges were mastered (at high prices), but their exploitation was lacking.
It was a distinctly different challenge to exploit breakthroughs and thus make them worthwhile. The attacker had to beat the defender in the race against the reserves. The re-establishment of the tactically so powerful front-lines needed to be delayed, the culminating point of attack had to be observed and to be pushed forward. The challenges were entirely different from the breakthrough challenges, and one would misunderstand the Inter-War Years' military progress if one had no concept of the difference between the breakthrough (a tactical challenge) and the purpose-giving breakthrough exploitation phase, the operational level challenge.
We could call this "breakthrough" and "exploitation" instead of "tactical" and "operational" in this specific case, but there are many such examples*, and it is the words "tactical" and "operational" which have assumed a meaning for use across very many examples.
It makes sense to use the mental construct of an operational level of warfare.
*: Napoleon's corps converging and the joint battle. Athen's expedition to Syracuse as a whole and its two specific battles. (Notice how pre-front lines there was first manoeuvres, then battle, then exploitation while in the age of front lines the first phase was rather a logistical build-up of the force concentration and of local stocks)..