Is it possible to commute 34 km (21 miles) daily?
That's similar to my old commute (a bit further but flatter), and I didn't cycle regularly when I started. The Google estimate is probably reasonable for the second time you do it, though may not reflect rush hour traffic. The first time will probably take longer due to unfamiliarity (a trip when it doesn't matter if you're late is helpful) and eventually you could be noticeably quicker.

You might get away without a shower in winter, if you're prepared to set off cold, but in summer it's another matter. Mild wet days are also sweaty. Is there a shower available?

When I started bike commuting that sort of distance it was quite tough. Having rest days in the first few weeks helped, and I found that a protein bar or flapjack immediately on arrival in the morning made the return leg (and the day in work) easier