Here's something few others have pointed out: religion. The main basis for science arising and becoming as widely accepted as it is today is astronomy. The early astronomers (Galileo and his contemporaries) pointed out that the Sun is fixed and the Earth revolves around it; they were shunned at the time for heresy and blasphemy. If we didn't have their theories, it is entirely likely that religion would dominate our lives today.
Furthermore, it is fairly likely that Christianity would be the dominant religion by far. It is as dominant as it is today because of the empires of Europe, of Britain, France, and Germany, with some Spanish influence. Without astronomy, you don't have anyone rejecting religion out of hand, so the influences Christianity left would have remained, leading to it becoming far more dominant. Other religions would still be observed, but in smaller less pronounced pockets.
Timings would also suffer. Calendars and, importantly, leap years are based on our observations of astronomical phenomena. One month (word origin: "1 moon" > "1 moonth" > "1 month") was originally defined as one cycle of the Moon, 28 days. Over time this definition has been revised to keep up with our other definitions, such as seasons.
Leap years are based on the movement of the Earth around the Sun. As detailed in this article, the Earth actually takes 365.24 days to make one full revolution around the Sun, so adding a day (February 29th) every 4 years keeps us about in sync. If leap years hadn't been invented but some form of rudimentary calendar had, people would get very confused as, over the years, winter moved to summer and summer upped and left to take winter's place.
You are, however, right in assuming that we would eventually make these discoveries. As I see it, this could happen at one of two points:
- By accident
If the world advances enough to have electromagnetic radiation sensing beams of the kind we have today, they might point one at the impenetrable cloud and find that there's something beyond. That would, of course, spark a massive space race.
- Manned flight
As you say, once humans invent the aeroplane (probably a little later than we did), they can easily fly above the clouds and observe. Again, the first confirmed occurrence of this would spark the space race, to see who could master orbital mechanics and get a satellite up first.
However the discovery of space is made, there's a lot of discoveries to be made until this society is anywhere near our understanding of the universe. They'll end up several hundred years behind on astronomy, but could well do better than us in other fields, having had more time spent on them because of not spending said time on space exploration.