The chimpanzee fossil-record is really poor; we don't have a good idea what chimps looked like back in the early hominin days, but its true that in the past few thousand years - a minor blip on the evolutionary scale- we've progressed and advanced leaps and bounds beyond them intellectually. However, as stated before, from the standpoint of our functionality as animals, we only have three real tangible advantages: we stand upright consistently, we've got better hands, and we're way more clever. Chimpanzees are stronger than us, they're more durable than us, they're generally faster, more agile, more dexterous than us, they resist the elements better than us, they're less prone to illness than we are. The presumption that we're 'More evolved' than chimpanzees is a misconception. It's not a race, and there is no finish-line. Chimpanzees just aren't evolving in the same direction as us, likely because of entirely different conditions/challenges/diets/necessities.
It's probable that at some point, early humans- already at least as clever as other primates- found themselves in a 'do or die' situation where they had to start hunting consistently to survive, in conditions and facing prey where 'run after it and pounce on it' simply wasn't cutting it anymore. We needed to be clever, we needed to use tools, and those early humans who excelled at this over others got to succeed in their hunt, feed their families, and become 'alphas' in their social structures, doing the most breeding. Hunted meat as a dietary staple means way more protein, which we know is essential to brain development from an individual standpoint, let alone on an evolutionary scale. Protein contains the amino acids like seratonin and tyrosine which make up our neurotransmitters.
Thousands of years of sneaking up on animals, hucking rocks at them, and reaping the protein-rich rewards- allowing the cleverest, most accurate rock-huckers to excel could easily have led to increasingly clever humans with increasingly robust and protein-enriched brains, and eventual epiphany moments over further thousands of years like 'pointy stick is better than rock', 'can use rock to make stick more pointy', 'rock and stick can be be combined, even better for hucking!' the whole time working out things which aid in their efforts like specific vocalizations to communicate more and more precise information over long range, eventually leading toward things like basic language.
As our brains become more and more robust, as we start developing language, we start having increasingly complex thoughts, and eventually develop the capacity for abstraction. We start having thoughts like 'What is this?' 'Why is this?' 'What am I?' 'Why am I?' and as we learn to relate these abstract thoughts to each other, we start dreaming up answers, which allows us to start structuring our societies in ways no animal has before, creating bonds and rules around ideas, rather than just pure animal necessity, a sapience which unleashed the power of our intellect, and allowed us to build simple social structures up into communities, communities up into civilizations, the rest, as they say, being history.
That, at least, is the most plausible scenario to my mind; more so than alien statues and finger-stretching god-things, and there's a fair deal of (to my mind) compelling evidence to support it.