Ox-drawn plows are at least 4000 years old, and I feel like seeing an animal pulling a plow all day begs for wheels so you can pull anything anywhere. At least more than the combination of a wheel and a stick, to apply mechanical advantage to lift and then move things.
The oldest wheelbarrow that we know of is from ~200 BCE, and the oldest chariots from ~2000 BCE. This tracks with animals pulling your stuff either being more obvious or to there being a higher ratio between payoff and cost of development.
You're right that it often comes down to dumb luck, but I think those lucky moments are usually facilitated by other factors. That's why there are often simultaneous and independent inventions (multiple discovery), and why tech startups aren't geographically uniformly distributed.