Huts and log cabins are perhaps not the best examples. While Germanic material culture and architecture was no doubt simpler than its counterparts within the Roman Empire it would be unfair to dismiss it all as huts and log cabins. While Germanic buildings were almost totally constructed out of wood, and thus they have by and large not survived to the modern day, there are actual examples of impressive structures coming from outside of the Roman world in Germanic contexts. There are two examples, one archaeologically confirmed (and recorded in written history) in Post-Roman Britain, and another that was written about in Pre-Christian Scandinavia.

I'm going to sidestep the issue of Germanic polities in relatively intact Roman territory, so no Goths, Visi or Ostro, no Franks, no Lombards, and no Vandals. That leaves us with the former Roman territory in Britain. Britain at the time of the western Roman collapse was in dire straits, an economic collapse, abandonment by Roman authority, and Germanic peoples washing ashore. However Roman influences still remained and interesting were imitated in many ways by the new comers. In one of the Anglo-Saxon kingdoms, Bernicia, later part of Northumbria in Northern England a royal complex with evidence of a series of large structures, including what appears to have been a wooden amphitheater. While not constructed out of stone or of a similar size to Roman palaces in Constantinople or Frankish ones in Aachen, it was still and undoubtedly impressive site.

According to the Venerable Bede, the royal site in Northumbria was abandoned after the Northumbrians embraced Christianity and they moved their royal complex to a new site. Scholars have taken the Yeavering site to have been that original royal complex.

A later account, dating to well after the collapse of Roman power in the west, but this time in a location that never saw substantial Roman influence is the temple at Uppsala as relayed by Adam of Bremen. While we need to understand that his depiction of the rituals and spaces at this site might not necessarily completely reflect reality, he had a vested interest in playing up their pagan beliefs to be particularly barbaric, it seems overly revisionist to me to flat out deny that impressive structures such as the one he describes could have existed as centers of worship.

The center he describes contains three statues of the primary deities, gilded work on the interior, and golden chain surrounding the center, as well as a giant evergreen tree. While the specifics of his account are up for debate, the amount of gold he describes certainly raises some eyebrows, the importance of the site as a center of worship is not disputed. While it is often assumed (and portrayed in media) that stave churches are the descendants of such pagan sites it has not been conclusively demonstrated. The exact nature of the site's construction and lay out will probably remain in doubt, but the existence of impressive cult sites in Scandinavia does not seem to be particularly controversial.

Both of these examples are from outside Germania proper and from a later date from the migration era and the collapse of Roman authority in the west, but I believe they are indicative of the kind of architecture and buildings that were possible in the Germanic world at the time of its interactions with the collapsing Roman world.