Normally I am most well-versed in Viet Nam from the Nguyen Dynasty to now, but this is a topic I actually happen to be very well-equipped in terms of resources to answer, so I will.

This question can be looked at in multiple ways. I don't want people to think that Vietic peoples did not exist prior to Chinese colonization of the area. They objectively did. Vietnamese people are the native inhabitants of what is now northern Viet Nam. They are Austroasiatic language speakers, which is the same family that includes Khmer (Cambodian), whereas Chinese languages are in a different language family altogether. However, if we are discussing if Vietnamese culture as we know it existed, in any amount, prior to Chinese colonization, then the question becomes much more difficult. The problem is that trying to determine whether a culture from modern times is the same as or descended from one from pre-historic times, it's pretty much impossible. China has, of course, had a profound influence on Vietnamese culture, but I think it would be incorrect to say that Viet Nam does not have an indigenous culture; generally when an area is colonized by another group, the group being colonized does not lose its own culture, and sometimes there is (smaller) influence in the other direction too. Generally, there is a certain amount of give and take by the colonized group in how the colonizer's culture is adapted to their own. That's the main word right there: adaptation of culture, not copying or replacement. One can only make educated guesses as to how this played out in the context of Vietnamese people.

This is a question less about history and more about archaeology and anthropology, and that is the academic content I am going to primarily use to answer this. So, with consideration that some respected historians do not believe there are significant prehistoric to modern cultural connections in Viet Nam, while others do, I turn to Nam C. Kim, an archaeologist who quite literally has written the book on prehistoric state formation in the Red River Delta. Kim acknowledges that this is an area of intense debate, among both scholars in Viet Nam and outside of Viet Nam (the Vietnamese state does not really censor these debates, thankfully).

Vietnamese legends and even national history talk about a polity named Au Lac. This is sort of taken as a kind of foundational kingdom. It was supposedly founded by An Duong Vuong. This is traditionally dated to around 258 BCE. Eventually it bacame part of Nam Viet, which had its capital in what is now Guangzhou, China, but it was not really what we would call a Han Chinese polity. These were mostly indigenous people from this kind of borderlands region, before Chinese speakers were the dominant demographic. In fact, the leaders of Nam Viet are called the Trieu Dynasty in Vietnamese tradition. Eventually Nam Viet was conquered by the Han Dynasty, which marks the first period of Chinese domimation in the region. Anyways, the capital of Au Lac was supposedly Co Loa. Co Loa is an archaelogical site in what is now Ha Noi. What has been determined is that this was a city, perhaps a seat of government, and it was likely developed around 300 BCE or maybe even earlier. This of course would naturally lead to people believing that Au Lac was a reality. It is definitely tempting to do so, however Kim stops short of that. His reasoning is similar to how some would not take the archaeological culture of Erlitou to be definitive proof of the legendary Xia Dynasty. There are possibilities, but no definitive proof. What is known is that Co Loa was real, was inhabited with people who are genetically and lignuistically the ancestors of people who live in the region today.

However, there is other tantalizing circumstancial evidence to go along with Co Loa. For example, there is a Chinese coin dated 200 BCE found in the Co Loa I drum at Co Loa, along with inscriptions written in Chinese on the drum. Is this potential evidence of the existence of Nam Viet, thus also suggesting the existence of Au Lac? The event of Nam Viet defeating Au Lac is in textual accounts and literary tradition, after all. Nam Viet has a firm archaeological foundation, but its existence at Co Loa is still a question. As of now, the historical/legendary sources are not totally supported by archaeology.

All this being said, a Red River civilization clearly existed well before Han Chinese conquered the area. Additionally, it has been shown time and again that conquered people do not simply have their cultures replaced by the colonizers'. The people don't necessarily disappear, and in the case of this region, the archaeological and historical evidence points to the continuation of local lifeways, with an infusion of Han cultural elements. To that end, Vietnamese and Chinese of the 1st millennium CE (which would be mostly the time of Chinese domination of the area) were aware of the bronze drums of Co Loa, and their historical weight. That is, the drums I mentioned earlier were recognized by Vietnamese and Chinese during the colonial period as having been part of a polity in the Red River Delta. The drums were recognized by the Han as symbols of indigenous power and authority, and there is even archaeological evidence of the Han collecting, cutting, and burying them. This supports a Chinese text, Hou Han Shu, which talks about how General Ma Yuan confiscated and destroyed the bronze drums during the 1st century CE. Actually, elements of pre-Han culture seemed to resurface during the Chinese domination, as well as immediately after it. For example, Co Loa seems to have been used by the leaders of the Early Ly Dynasty (6th and 7th centuries CE). In addition, at the end of all the Chinese domination periods, none other than Co Loa became the capital of the newly independent Ngo Dynasty. Ngo Quyen proclaimed independence and sovereingty for Viet Nam in 939 CE, and chose Co Loa as the capital. Certainly, these sorts of events would suggest that memories of the past survived in some cultural practices, beliefs, stories, and traditions, despite Chinese presence and authority. Additionally, the Later Ly Dynasty (11-13th centuries CE) encouraged the collection of artifacts such as bronze drums as a way to help legitimize itself as a new state by drawing connections with the pre-Han past. Not only is this awareness of a pre-Han past, but it is active preservation and perpetuation of knowledge of that past.

As a sort of side note, there are groups of people in the highland and borderland regions who experienced different kinds of cultural influence from China. For example, there are still groups who practice the tattooing traditions that are/were found throughout Southeast Asia, including in the Philippines and Indonesia. This is not generally seen as a Han practice. Of course, this doesn't mean that these groups are representative of what Vietnamese people may have looked like before; culture is not static, and those groups are no more static than the lowland Kinh Vietnamese are.

Ultimately, we really don't know how much pre-Han culture exists in modern Viet Nam. It's probably impossible to know. However, what we do know is that throughout Viet Nam's history, there has absolutely been a feeling of continuity with the pre-Han past, despite all of the likely massive changes the society endured. The Vietnamese people of the the post-independence dynasties seemed to have felt they were the same people as the ones of pre-Han Viet Nam. This is a feeling that exists to this day.

The source I used most was The Origins of Ancient Vietnam by Nam C. Kim