Stoke brokers generally match buyers to sellers, so normally you are buying someone else's shares. If there aren't enough shares for sale, then the price will go up until someone is willing to sell shares to meet the order. If you're trading a very large chunk of stocks you may decided to do it through a private market (e.g. dark pools).

During an IPO, the create new shares that the company sells to raise money. People are buying these shares from the company until there are no more shares and people start buying each other's shares again.

Another option for listing besides an IPO is a direct listing. Here new shares aren't created. The privates shares by the company investors and/or employees are now publicly tradable, and they trade like a normal stock transaction.

One reason people may choose to sell quickly for a lower price is taxes. If you have pre-ipo options (right to buy stock at a given price--this is commonly how stocks are offered to employees of a start-up company), then once you exercise those options (which you generally required to do if you don't want them to expire worthless) you have a taxable event. The taxes can be considerable. Your stocks may make you a paper millionaire, but you may have a six figure tax bill incoming. Unless you are a very high level executive (or investment bank) your shares likely have a 6 month or so lock up period during which you aren't allowed to sell your stocks (this is to allow the upper level people to make their money without the peons putting downwards pressure on the market by selling their stocks. These peons still have the tax bill, so when the lockout period expires you'll see a lot of selling of the stock as peons try and sell stocks to cover their tax obligations.