Note that even that "money in the bank" of traditional venture firm is not really money in the bank. VC, PE, and hedge fund managers usually don't have all the cash for the fund sitting in the bank at all times. Rather, their agreement with the LPs that fund the fund is structured as a series of capital calls: it gives the fund the right to demand that their LPs deposit cash in their bank accounts within 10-30 days, which can then be used to fund the investments that the VC firm makes. The capital calls are backed by legal documents enforceable in court, with pretty stiff penalties for failing to meet a capital call.
Such a funding structure here isn't all that different: the funding agreement gives OpenAI the right to call on their backers to make certain cash deposits, contingent upon milestones being met. Deep down inside, "money in the bank" doesn't actually exist, it's just mutual agreements backed by force of law.
When a startup raises money without contingencies, typically they do get a large amount of money in the bank all at once.