Polytheism did exist before collision of the Romans and the Celts and Nordics, and even before the Celtic and Nordic cultures had existed. This isn't technically "proven" because the cultures prior to the Archaic and Classical Europeans didn't actually have a writing system, at least none which there is evidence for.
Instead we've made strong inferences about Proto-Indo-European culture based off of similar lingual structures of Native European and Vedic languages. Ferre in Latin has some similarities to the Old English word Beran. The word Zeus seems to have Etymological similarities to the Germanic Deity's name Tiw/Tyr, Roman Jupiter (from Archaic Latin Diovis [pater]), Celtic Dagda etc. so we can infer that they came from a common source.
Similarities and patterns in Proto-Indo-European based religions also lead us to believe that the deities and pantheons are (for lack of a better term) spin offs from an original pantheon. I'll give a few examples.
There is a pattern of a sky father with the lingual root De[w] (as seen in Greek Zeus, Roman Jupiter and Germanic Tiu), a pattern of divine twins (Greek Artemis and Apollo, Germanic Freya and Freyer and Roman Diana and Pheobus), other divine twins or smply siblings with solar/lunar qualities (Greek Helios and Selene, Roman Sol and Luna and Nordic Sol and Mani). There also is a pattern of a divine queen (Greek Hera, Roman Juno and Germanic Frigga) an Earth Mother, usually simply referred to as "earth" in whatever language the deity is revered in (Jord/Eorth to the Germanic peoples, Terra Mater, literally "Earth Mother" in Rome and Gaia in Greece). A different goddess of the earth and Fertility (Germanic Nerthus, Celtic Danu, Greek Demeter and Roman Ceres). Another pattern is a masculine deity of fertility which usually, but not always has an association with Thunder or lightning (Celtic Taranis, Germanic Thor/Thunar, Vedic Indra and [possibly, but uncertainly] Greek Dionysos and Roman Bacchus).
I could literally go on forever. We see however that by breaking the theology, mythology and linguistics of deities, we see more and more that it is at the very least highly likely that these gods have a common origin. So just because a hymn to Thor wasn't written down before say the Viking age, we know that the praises to The Thunder God was being practice long before Imperial Rome had any conflicts with Germans or the Gaulish.
Another note: We actually DO have written and archaeological evidence of polytheism before Rome's conquest throughout Europe, just not within Europe itself. We have ruins and actual translated texts of Egyptian holy books (such as the Egyptian book of the dead) which are dated to be written at least 3550 years ago, much longer before imperial Rome. Granted it wasn't IN Northern Europe, but the polytheism that existed a long long time ago in places like Egypt, Japan, India, The Americas etc. leads us to believe that we as humans remained consistently polytheistic for thousands of years since we were in Africa. This is a root belief in humanity, it's practically in our DNA.
I'm not trying to proselytize, just pointing out the cultural and linguistic theories and facts.