Germania had some resources that would be useful to the Romans
It would necessit several things.
1) Romans knowing about these ressources
2) These not being avaible more easily either by trade or within territories already controlled by Rome
3) Presence and/or creation of infrastructures
4) Being worthile enough to justify investement in time and ressources (at some point, it's only the case for luxury products, meaning amber or furs)
Main motivations would be shortening the border and eliminating barbarian threats.
Romans did have a really particular sense of geography : for centuries, Romans pictured Gaul atlantic coast being faced North. So, don't think of a geostrategical point (admitting Romans did adopted one) with a modern map.
Romans, when searching for borders, searched for defensible ones : Rhine, Danube were good borders as hard to cross. Random point on Germanic plain or forest on the other hand...
As for Barbarian threat, which one exactly? Before the IIIth century crisis, regular raids/campaigns at worst, exchanges usually were enough to keep order on the border.
Admitting that Romans didn't understood that, however far they would advance, they would still face hostile people, they wouldn't have seen in Germans an actual factual threat for their domination : at "best" as a great annoyment that should be watched in case of someone willing to pull a Cimbri and Teutoni.
They did for Gaul (and more because of historical traumatism and paranoïd propaganda), or Dacia (that admittedly formed relativly unified ensemble), but Germans? Look at what Tacitus accounted for, and you'll have an idea of how the average Roman tought : poor devils living in dark swamps or forests.
Eventually, the simplest and easiest explanation, will of conquest, demonstrating Roman dominance, would be probably the most plausible motivation and not only because the others wouldn't work well. It was an actual drive for Romans, critically with emperors in need of legitimacy as it happened for Brittania.
The Romans could build roads, infrastructure ect.
They rarely did it out of nowhere, and essentially in mediterranean features.
Remember that mediterranean climate (and agricultural region) limit was more north than today, and that Dacians or Gauls had already develloped their own regions before Romans (both politically, and regarding infrastructures).
In Germania, almost everything had to be done from scratch : think of northern Brittania devellopment, that is really limited compared to western continental's.
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As it was suggested : a good contact possibility between Jutland (I assumed, maybe wrongly, you wanted a contact with modern OTL Danemark and not the ancient Danes Germans) would be trough Frisian coast, and save you expeditions/conquest and all in Germania Magna.