What do you mean by ‘valid’? These are reasonably well-defined groups. The Belgae a bit more complicatedly so, but the Celts and Germanic tribes being defined principally through their use of the well-defined Celtic and Germanic branches of the Indo-European languages.

I think you mean to ask, ‘Are these terms that the ancient groups would have used for themselves as a whole, or do they correspond to identities they would have chiefly recognised?’ And the answer is... complicated.

Now some academics object to the use of the term ‘Celt’ on the grounds that we have no real examples of very ancient use of the term by the ‘Insular Celts’ (ancient Britons, Irish and probably Picts) for themselves, and though from a linguistic standpoint their languages were certainly Celtic, it’s not extremely clear how to place them within that - a whole other topic. Rather, the name is Greek, and seems to correspond to the Gauls (Caesar even said that the Galli called themselves Celti), and was later applied by the Romans to the ‘Celtiberians’ of Spain, who we know spoke another, rather different, Celtic language.

So the concept is valid, and at least linguistically and culturally they derived from a Proto-Celtic culture (perhaps part of the regionally prehistoric Urnfield, then Hallstatt cultures - and the Gauls corresponding to the La Tène culture) - the term is not one they would all necessarily have recognised, however, but it is at least a candidate for the original Celtic ‘endonym’.

‘Germani’ is a Latin word, but also applied to what we would now see as a common larger group of people with a shared Proto-Germanic language, which unlike the Celtic languages was still quite unified when they arrive in the historical record, significantly splitting only around the time of the Great Migrations. They also had a common religion and set of other social norms and customs that are better attested. The large amount of contact within the Germanic world - for example the existence of mixed bands during the Great Migrations and the common epics across this ‘Germanic world’ we even see in Beowulf - show that there may have been some sense of unity. And we have every reason to think that this may have applied to the prehistoric Proto-Celts as well, to the extent that their language was by definition common. However, we have no specific early endonym for them either - the Roman name Germani may be Latin, the ‘Teutoni’ is based on a particular ancient tribe, as are the cognates of the ‘Allemani’ like French ‘Allemagne’ - a confederation possibly meaning ‘all men’, etc. The closest is probably the ancestor of Deutsch/Duits/tysk, from Proto-Germanic ‘theudo’, meaning something like ‘nation’.

The Belgae are portrayed by Caesar et al as a real political confederation with links in Britain and which united certain Celtic and Germanic tribes. John Koch sees ‘Belgae’ as a possible cognate of the ‘Fir Bolg’ in Irish mythology. In any case, we have no reason to think this identity is ‘invalid’, even if there were multiple identities at play, just as a Swiss person can also be Bernese, or German-speaking or French-speaking.

There is also the (very) controversial theory of the ‘Nordwestblock’ by Kuhn and Gysseling that there was once an intermediate Belgian language or at least Indo-European branch in that transitional Celtic-Germanic zone, possibly preceding and influencing the Belgae.

All this considered, the terms are valid in a modern sense and I don't think we can sag they were invalid concepts even in an ancient sense, at least in their early stages, even if different words were used and other, more specific, tribal identities were more immediately important in the Roman period. It’s worth noting though that some ‘boundary’ tribes have been labelled Gauls or Germani based on their location or allegiance, like Germanic groups within the Belgae, or the confusion in the modern era over the Cimbri and Teutones (for a while it was seen as likely that these were both really Celtic, which would make ‘Teutonic’ a rather awkward term, but the current consensus is that these were more likely Germanic after all, the confusion stemming from the fact that this was the first very major encounter the Romans had with Germanic tribes in an area of northern Italy where they had had trouble with Gauls).