I find it very difficult to talk about ethno-linguistic groups or ethnogeneses here, because we have no evidence that there ever was such a thing as a 'Germanic' or 'Celtic' ethnic group - we are purely talking about linguistic groups here.

The Celtic languages have some features in common with the Romance branch of Indo-European, which have led scholars to propose an 'Italo-Celtic' subgroup of Indo-European (which would mean that the Romance and Celtic branch spent some time in close vicinity after separating), but this has been increasingly challenged (particularly by Calvert Watkins), although there are still scholars adhering to this view.

Some people equate the 'spread' of the 'Celts' with the expansion of the Hallstatt and La Tène archaeological cultures in central/western Europe, but there are huge problems associating archaeological 'cultures' with the spread of languages without any additional evidence - there are enough cases where languages spread without the material culture changing and the other way around to make this hypothetical at best.

The earliest evidence for Celtic languages are the Lepontic inscriptions in the Italian (and Swiss) alps from the second half of the 1st millennium BC and Gaulish texts from France and northern Italy. Slightly later (2nd century BC) Celtic inscriptions are known from north-central Spain (Celtiberian), and Brittonic is attested in Britain in the Roman period. We also have some evidence for Galatian in central Asia Minor and Noric in Austria/Slovenia. So what we know for sure is that by the 6th century Celtic speakers were present in a sizable portion of central Europe.

The case for Germanic is even more muddled, as people tend to conflate archaeological and linguistic evidence even more and we have less direct evidence. An often proposed homeland for the Germanic languages is Northern Europe (particularly northern Germany and southern Scandinavia), based, among other things, on early loans into neighbouring languages. Germanic languages are not very well attested before the 4th century AD (the Bible translation into Gothic): there are a few words and place names in Roman sources and a few scattered inscriptions from the 2nd century AD onwards. It is thus incredibly difficult to reach far-reaching conclusions here...

The question of the Indo-European homeland itself (and whether or not one should even look for one) is still heavily debated and there is by no means a consensus regarding the Pontic/Ukranian steppe...

So, the bottom line is that we can't really pinpoint where individual Indo-European languages split up - but it is clear that we are dealing with a gradual 'split' over longer periods of time and that not all languages branched out at the same time.

Some references for further reading: Ball & Müller (eds.): The Celtic Languages. (particularly Chapter 2 by J.F. Eska: 'The Emergence of the Celtic Languages') König & van der Auwera (eds.). The Germanic Languages (particularly Chapter 1 by Henriksen & van der Auwera 'The Germanic Languages') J. Clackson: Indo-European Linguistics. An Introduction. Particularly pp. 5-19