When would giant companies ignore the small companies that are growing fast?

I have made a claim that large companies will grow larger and larger and the only opportunity that small businesses may have to grow to become giant companies is that they grow fast enough in order to become large enough before being noticed by the giant companies. However, I would like to add more details about how possible small businesses could be ignored by the giant companies when growing in their markets.

There are several situations that giant companies might ignore the small businesses that are growing fast. Firstly, when giant companies do not understand the potential of a market, they will not be interested at investing in the new market, of course, they will not try to acquire the businesses in the market. This gives the small businesses in the market more time to grow bigger. When a market is completely new because of innovative technologies, no one knows what to do with the new technologies. Secondly, when giant companies believe it is too risky to invest in the new market, they will not be interested at investing in the new market. The risk comes from the uncertainties of the future and the initial investment. When the expected return is smaller than the initial investment, the giant companies will not be interested at investing in such market. Thirdly, when there are too many opportunities at the same time that all giant companies together do not have sufficient finance to invest in all sectors which have opportunities. Such circumstance only happens when the speed of innovation is much faster than the previous level. If we assume that previously the markets were dominated by the existing giant companies, it means that the giant companies had sufficient resources to invest in all sectors where have innovations; however, once the speed of innovation suddenly increases dramatically, the initial resources held by the giant companies are suddenly insufficient to support them to invest in all sectors where innovations take place. Under such circumstance, the businesses in some sectors are possible to grow independently from the giant companies and potentially able to become giant companies themselves.

To conclude, it is not entirely impossible for small businesses to become giant companies themselves, especially when there is a technology boom that giant resources are not possible to invest in all sectors where technology innovation takes place.