A large part of what makes a tribe a tribe is common language. People living far enough apart create differences in pronunciation that serve as markers for in-groups and to hear immediately if someone is foreign. Subsequently a restricted flow of people across geographic barriers (mountains, Big rivers) which acted against the exchange and assimilation of language also created barriers between people. Another is common decent, real or mythical, which is also facilitated by geographic barriers. Since those existed in prehistoric times, I think it's quite likely that we have tribal-like societies since the introduction of sedentary lifestyle in the beginning of the early neolithic age.

Following that logic, a tribe might have been just as old as the last large migration of people into that region. There have been several migrations being postulated because of shifting material culture, but it is very uncertain because you can't exclude that the same people just started using different things. One prominent example is the Amesbury Archer who came from continental Europe to England with a probably migration of Bell Beaker people. But even those examples don't lend themselves to stretch interpretations from one individual to the whole group.

what was that tribe, did it exist in the stone age?

We don't know a lot about the organisation of stone age society, at least now enough to clearly answer the question. The earliest written sources are from classical antiquity from heavily biased roman or greek authors.

In prehistoric archaeology we can differentiate material cultures that share similar styles of pottery and later, metal artifacts. Those have often be used as a hint towards ethnic groups, but it is very unlikely that those represent what one could call "tribe", given that archaeology has a hard time differentiating the material culture of different historic germanic tribes.

Hints towards how stone age society was structured can be the massive earthworks and megalithic structures. It is likely that large amounts of people came together from a larger region to construct them, they must have had some common ground.

In the late bronze age and the following iron age we have very prominent burials of individuals that are recognizable as elite. You could infer from that that those probably dominated a coherent group of people. Unified leadership is a hallmark of the historically traceable germanic tribes. There are a few specialised burials in the late neolithic and bronze age. It's hard to say how egalitarian the stone age people were. So the trend of tribes as political structure could have extended into the bronze age at least.