You'll have a professional do the corporate taxes. Briefly, you'll expect that for the first several years of the business, possibly continuing through exit, the business will have negative profits. Accordingly, your
income tax bill
for the corporation will be $0 every year. You'll expect to continue booking tax losses as an asset on the balance sheet against that day in the future when your business actually has profits. You will likely pay many taxes which are not founded on income, most prominently California franchise tax for YC startups, which has a minimum of about $1k a year or so.
The fact that the corporation received $120k from YC or $10 million from angel investors is immaterial. Those flows of money do not represent revenue/profits. They are not subject to income tax (nor any other tax that I am aware of).
The approximate runway of a company with $120k in the bank and 2 co-founders at ramen wages with $1k a month in OpEx is ~18 months as of the current moment in time. Napkin math: $6k to pay both founders ~$2k salary plus pay direct costs of employing them, $1k in OpEx, divide.