In a situation of true free trade, which is to say a system of permanent competition, all industrial success is necessarily temporary. Products and business models always end up becoming obsolete, replaced by new products and services that are better and/or less expensive. Certain unscrupulous industrialists know this and try to get governments to impose legal barriers to entry into their markets. In this way, they try to protect their turf by reducing the possibility of new competition.
In the absence of such artificial barriers, potential competitors, stimulated by the success of their predecessors or frustrated by the state of the art of available products, do what it takes to conquer the hearts and minds of sovereign consumers. As shown by the story of the founders of Apple in their garage, or of Xerox in their kitchen, your starting point in the race to the top is no indication of where you end up.
Therefore, when we observe the success of a given company, we need to ask ourselves whether this success has been achieved and maintained through innovation and progress benefitting consumers, or if it has been maintained by a regulation that prevents a competitor from proposing something better.
In the case of Google, there is no law preventing anyone from developing a better business model or a more cutting-edge search engine algorithm. There are in fact alternatives that are preferred by a certain minority of consumers. A large market share at a given moment in time does not in itself mean that a company can dictate market conditions. It is consumers who dictate those conditions, as they judge that they do not prefer other available options.
Anti-trust laws completely ignore the existence of potential rivals and the very real threat they pose to established producers, despite innumerable historical examples. Breaking up Google would not improve the choices available to consumers, nor the competitiveness of its rivals. It would just reduce its ability to innovate in the short term, and indirectly, the well-being of the customers who would have benefitted.