If the company is valued by the underwriter and initial buyers at $1 trillion and the company offers 10% for sale through their underwriters (who have put out feelers to try to attract buyers at highest price possible), they raise $100 billion from the offering, minus fees, to use as needed to further the business. The initial buyers get the shares at that valuation, and I believe if the underwriter positioned it wrongly they might be on the hook to sell some shares at a lower price without prejudice to the company.

If one of the initial buyers sells in the first minute the company is public the first publicly traded shares at 1.5x their purchase price, the company suddenly has a market cap of $1.5 trillion instead of $1 trillion, and that buyer has made a tidy 50% profit on the shares they just sold. If all initial buyers dump a bunch of their shares the price likely will go down, perhaps pushing the market cap to, say, $750 billion. Regardless of this action on the first day and after, the company offering their shares still has the $100 billion.

Note that initial buyers are discouraged from selling large portions of their shares.