It can be done. The Hitchhiker's Guide to the Galaxy is one of my favorite novels, and its protagonist, <PERSON>, does not have a goal throughout the first book, other than surviving the few dangerous situations he winds up in.
The reason this works is because the book was never about <PERSON>'s character arc. The book is first and foremost a comedy, so as long as we're laughing, we don't care much about what happens to <PERSON>. Second, the book is a satire highlighting the various similarities and contrasts between <PERSON> galaxy and the world we live in. <PERSON>'s journey only gives us an excuse to peek into various facets of life in the galaxy through the eyes of an outsider.
And, indeed, this is a big reason why the movie version was a big flop with me, because they tried to make the movie about the story, and they cut out many of the jokes and satirical elements to keep things moving along. The result was a story that was much more dramatic, but not any more interesting, and certainly not any more fun to watch.
I would be remiss not to add that, as the series progressed, <PERSON> did start giving his stories meaningful plots and character arcs, and then the reader does care about what <PERSON> wants and what he does about it. I think the series improved for it, but the first book nonetheless showed that such things are not strictly necessary. 190
It's also worth noting that the first book was mostly an adaptation of a radio series, where it's easier to get away with writing sketch comedy even if your show is not technically a sketch comedy show. The parts that were not adapted from the radio series tend to adhere much closer to traditional storytelling.
In any case, if your story is not a comedy, then it would be much harder to make this work. For each scene in your story, you need to ask yourself, "Why would the audience care about this scene?" For Hitchhiker's, the answer is simple: the scene is funny. So long as the audience laughs, you win. But there isn't a comparable analogue for drama. You don't automatically win when the audience gasps or cries. You don't win until you give them catharsis, so everything in your story needs to work toward giving it.
This usually means having an arc that you can resolve, and that usually means having a character drive that arc. If this character isn't your protagonist, you might want to consider changing your story's point of view so that it is. 38