Long story short - they did invade from other areas, depending on the military need. You have to bear in mind that there was no single Germania, in the sense of a modern state. There were many tribes, who controlled varying amounts of territory. Roman expeditions were usually against such tribes, and the direction of attack would vary because of this.

The alps were not a problem. The Romans actually held significant parts of what is today southern Germany and Austria (thus, north of the alps), with the Danube being the principal border. Wikipedia has a nice map that shows the Roman provinces (a bit later than the era of Augustus, where most campaigns into Germania took place). You can see the alps as grey-shaded mountains, and many Roman cities north or northeast of them, such as Augusta Vindelicorum (today's Augsburg), Vindobona (today's Vienna), Iuvavum (today's Salzburg).

One of the largest invasions took place in 6AD. It was aimed at crushing the Marcomanni (see map above). Roman generals Tiberius and Sentius Saturninus invaded with a total of 12 legions - 6 under Sentius Saturninus from Moguntiacum (today's Mainz, so from the West), and 6 under Tiberius (from Carnuntum, which is near today's Vienna, so from the south). This was a gigantic, two-pronged invasion - but it came to an end when a revolt broke out in the Roman province of Illyria and Tiberius had to rush back to quell it.

Other expeditions, aimed at other tribes and areas. The Battle of the Teutoburg Forest was part of a campaign against the Cherusci and their allies, which is why it took place from the West.

(I don't have my in-depth sources on me, as I'm writing from the office, but I can add them later if requested/required, I did double check the campaigns with Graham Sumner's "Die Römische Armee", just to be sure).