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We have written accounts of Gothic language from 4th century onwards. There are also sporadic written accounts of Western and Northern Germanic languages in Runic alphabet from 2nd century onwards. Procopius, in 6th century, mentions that Vandals and Goths are related (and also puts Gepids and Visi(goths) in the same basket, but not other Germanic peoples).
Pliny specifically puts Suebi into the Irminonic tribes, which are also identified as a group by Tacitus and Pomponius. Area inhabited by Irminonic tribes underwent the High German consonant shift before 6th century, which can be seen from the change in spelling in inscriptions compared to other West Germanic dialects.
Germanic languages show common Celtic loanwords, some of those related to technological inventions related to ironworking. iron itself is a Celtic loan, which implies it was introduced to Germanics by Celts. Those loans can be identified because they didn't undergo the regular sound shifts from Proto-Indo-European to Proto-Germanic, but later underwent the same sound shifts as Germanic words when the language developed further, diverging on the way. This puts a constraint on when Germanic languages diverged, it should be around the time of Hallstatt culture, and certainly not before the time of Urnfield culture, because that's when iron was first sporadically used in northern Europe. This means a common Germanic language must have been spoken as late as 800BC and likely even later (most sources give around 500BC for time of such linguistic contact).
Slavic languages, meanwhile, had a common linguistic development with regular sound changes in pre-Slavic place names until around the time of Charlemagne. The time period of development of Slavic languages until present is therefore similar to the time period of development of Germanic languages by the point of migrations. Of course, languages don't all change equally fast, most notably the rapid development seen in English (along with hybridization of vocabulary with French). But when there's no big external factors involved, and when there's no geographical isolation, we can assume language evolution happens at a similar rate.